Simplifying Rational Expressions: I need answers for both 7 and 8 below. Answers for just one or the other is also fine.

Answer:

7625597484987 ways

Step-by-step explanation:

Given the following :

Number of ball(k) = 9

Number of bins (n) = 27

How many different ways are there to distribute these 9 balls among the 27 bins.

Here, the balls have different labels (1 to 9)

The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.

Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k

27^9 = 7625597484987 ways.

Answer:

i think its 67600

Step-by-step explanation:

100*26=2600

2600*26=67600

Answer:

A(t) = R -5(t)

t in minuto

Step-by-step explanation:

Nesta questão, estamos preocupados em estabelecer uma lei que forneça a quantidade de água presente no reservatório a qualquer momento, usando a quantidade inicial de água no reservatório e a taxa de perda de água do reservatório.

Agora, sabemos que a taxa de perda de água é de 5 litros por minuto.

Assim, podemos estabelecer a lei da seguinte forma; vamos chamar a quantidade de água a qualquer momento no reservatório A (t);

A lei é assim; A (t) = R -5t onde t representa o tempo que estamos considerando e é em minutos, enquanto R é o volume inicial de água no tanque.

Answer:

17.3 = AC

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan B = opp/ adj

Tan 68 = AC / 7

7 tan 68 = AC

17.32560797 = AC

To 1 decimal place

17.3 = AC

Answer:

Step-by-step explanation:

To find AC we use tan

tan ∅ = opposite / adjacent

From the question

AB is the adjacent

AC is the opposite

So we have

tan 68 = AC / AB

AC = AB tan 68

AC = 7 tan 68

AC = 17.32

AC = 17. 3 cm to one decimal place

Hope this helps you

Answer:

the sum of p amd 7

hopefully this helped :3

Answer:

D

Step-by-step explanation:

Since addings answer is a sum

p+7

D

Answer:

Hey there!

S would be 2 times 7, or 14.

Hope this helps :)

Answer:

14

Step-by-step explanation:

This is a 30-60-90 triangle, so the sides corresponding are x, 2x, and xsqrt3. the side, s, that we want is the 2x, and the x is 7. So, s is 14.

Answer:

here,

money spent in 1st year =$250

money spent in 2nd year=$295

total inflated amount=$295- $250

=$45

Then,

inflation rate= ($45/ $250)×100%

=18%

Answer:

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Step-by-step explanation:

If a complex number is z=a+ib, then the trigonometric form of complex number is

[tex]z=r(\cos \theta +i\sin \theta)[/tex]

where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].

The given complex number is -5i.

It can be rewritten as

[tex]z=0-5i[/tex]

Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.

[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]

[tex]\tan \theta=\dfrac{-5}{0}[/tex]

[tex]\tan \theta=\infty[/tex]

[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex]    [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]

[tex]\theta=\dfrac{3\pi}{2}[/tex]

So, the trigonometric form is

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Answer:

in degrees the answer is 5 (cos 270 + i sin 270)

in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))

Step-by-step explanation:

Answer: Mass of a typical house cat:

Automatically eliminate B and D since they are not metric unit for mass

So, that leaves us with A and C. And since a cat is not huge nor weighs that much, the most reasonable one would be to measure it in grams.

Correct answer: C

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.

From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;

c² = a²+b²

100²  = 96² +b²

b²  = 100²  - 96²

b²  = 10,000 - 9216

b²  = 784

b = √784

b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity

According to TOA, tan B = opposite/adjacent

tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given b = 28 and a = 96

tan B = 28/96

tan B = 4*7/4*24

tan B = 7/24

Answer:

He hiked 10 miles.

Step-by-step explanation:

rate x time = distance

The distance up and the distance down are equal

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

Answer:

x = 3.25

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is the order of operation.

First, subtract 3 from both sides of the equation:

4x + 3 = 16

4x + 3 (-3) = 16 (-3)

4x = 16 -3

4x = 13

Next, dvide 4 from both sides:

(4x)/4 = (13)/4

x = 13/4

x = 3.25

x = 3.25 is your answer.

~

Answer:

x = 3.25

Step-by-step explanation:

4x + 3 = 16

4x + 3 - 3 = 16 - 3

4x = 13

4x/4 = 13/4

x = 3.25

Answer:

Step-by-step explanation:

Given the expression after 4 has been subtracted from both sides as

1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;

1/2 x + 4 = - 1/2 x + 4

x/2 + 4 = -x/2 + 4

Find the LCM of both equation;

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

Multiplying both sides by 2 will give;

x+8 = -x+8

Collecting the like terms;

x+x = 8-8

2x = 0

x = 0/2

x = 0

Hence, the value of x is 0

Answer:

0

Step-by-step explanation:

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

Answer:

[tex]\large \boxed{\sf \bf \ \ \text{The solutions are }(2,4) \text{ and } (-2,-4) \ \ }[/tex]

Step-by-step explanation:

Hello, this is the same kind of question that you have already posted( brainly.com/question/17141820).

I would suggest that you check my previous answer and try to apply the same logic here. When you try it if you have any question please let me know. It will be the more efficient way for you to learn how to solve it by yourself.

As I have already provided details for the previous question I will be more succinct here.

Again we can write y = y and then we have to solve the following.

[tex](x+1)^2-5=2x\\\\x^2+2x+1^2-5-2x=0\\\\x^2-4=x^2-2^2=(x-2)(x+2)=0\\\\x=2 \ \ or \ \ x=-2[/tex]

The solutions are (2,4) and (-2,-4)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

see explanation

Step-by-step explanation:

Under a rotation ( clockwise or anticlockwise ) about the origin of 180°

a point (x, y ) → (- y, - x ), thus

A(5, 3 ) → A'(- 3, - 5 )

B(8, 10 ) → B'(- 10, - 8 )

C(11, 3 ) → C'(- 3, - 11 )

Answer:

Current price $50eax135hats= $6750

Step-by-step explanation:

If he sells the hats at $52 he sells 3 less hats so $52x132=$6864

if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc

$56 x 126=$7056

Answer:

69.7° (corrected to 3 significant figures)

Step-by-step explanation:

Use the cosine formula to solve for x.

[tex]cosA=\frac{(b^2+c^2-a^2)}{2bc} \\cos x =(3.5^2+ 3.5^2 -4^2)}/[2(3.5)(3.5)]cos x =0.346939\\x=69.7[/tex]

Answer:

a) A quadrilateral with 4 right angles

Answer:

I think the answer is b

I'm sorry if I'm not correct

Answer:

B

Step-by-step explanation:

sqrt30 -6^2 doesn't work

2.5 sqrt18 and 5 do work

Answer:

-1/6=-0.166

-2/3=-0.66

Step-by-step explanation:

-by looking carefully you will notice that . which number is greater and smaller.

Answer:

-1/6 is greater than -2/3

Step-by-step explanation:

Answer:

The larger canister has 8 times the volume and 4 times the volume of the smaller one.

Step-by-step explanation:

The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.

The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.

The canisters are in the shape of a cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

The surface area of a cylinder is given as:

A = 2πr(r + h)

SMALLER CANISTER

Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres

Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres

LARGER CANISTER

Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres

Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres

By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

1. a=9     2. f=1    3. b=6

Step-by-step explanation:

1.) 4a-1=3a+8

subtract 3a from both sides

a-1+8

add 1 to both sides

a=9

2.) 1+f+3+f=f+5

combine like terms that are on the same side

2f+4=f+5

subtract f from both sides

f+4=5

subtract 4 from both sides

f=1

3.) construct a equation

b+5=11

subtract 5 from both sides

b=6

Answer:

1) The correct option is the third line

2) The correct option is the third line please see attached graph

Step-by-step explanation:

For the system of inequalities,

7·x > 21 or 6·x -9 < 21 we have;

7·x > 21

x > 21/3 = 3

x > 3

Also we have for 6·x -9 < 21 we have;

6·x -9 < 21

6·x < 21 + 9

6·x < 30

x < 30/6 = 5

x < 5

The representation of the region x > 3 and the region x < 5 on the number line consists of indicating points 3 and 5 with  circles not filled to represent less than < and not less than or equal to ≤ and shading the potion of the number line in between the two points

Which gives the correct option as the third line which has an open circle at point 3 and 5

b) To graph the inequality v + 4 > 2 and 8·v - 20 ≤ 36

For the inequality v + 4 > 2, we have;

v > 2 - 4

v > - 2

For the inequality 8·v - 20 ≤ 36, we have;

8·v - 20 ≤ 36

8·v  ≤ 36 + 20              

8·v  ≤ 56

v ≤ 56/8

v ≤  7

The region representing v > -2 or v ≤ 7 on the number line consists of indicating points -2 with a circle (not filled) to represent less than < and point 7 with a filled circle to represent less than or equal to ≤ and shading the potion of the number line in between the two points

Which gives the correct option is the third line which has a closed circle at point -2 and an open circle at point 7

Answer:

1) A. y= (20 - 2x) /5

2) C. 141.3

3) True ( Your answers are here.)

Answer:

1. is A 2. is C 3. is I believe True

Step-by-step explanation:

1.

2x + 5y = 20

-2x          -2x

5y = 20 - 2x

/5          /5

Answer: y = 20 - 2x /5

2.

V = πr^2h

π=3.14  r=3  h=5

3.14*3^2*5

1.413*10^2 which = 141.3

3.

I am not completely sure but I think it is True

Hope this helps

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

Answer:

Step-by-step explanation:

[tex]24\% \: of \: 800[/tex]

By definition of p% = p/100

[tex] = \frac{24}{100} \times 800[/tex]

Reduce the numbers with Greatest Common Factor 100

[tex] = 24 \times 8[/tex]

Multiply the numbers

[tex] = 192[/tex]

Hope I helped!

Best regards!!

Answer: a) $1,210.20     b) $313.20

Step-by-step explanation:

a) $87 down + $46.80(24 months) = $1,210.20 total paid

b) $1,210.20 - $897.00 = $313.20 interest paid

Answer:

x = - 1/18

Step-by-step explanation:

Move all terms not containing  x to the right side of the equation

Divide each term by 18 and simplify

The result can be shown in multiple forms

x = -1/18

Decimal form= -0.05

Answer: x=-1/18

Step-by-step explanation:

18x+18=17

you subtract 18 from both sides

18x=-1

then you divide by 18 on both sides

x=-1/18

Answer:

Step-by-step explanation:

Given

u = 14 , a = 8 , t = 4

Now, let's find the value of s

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

plug the values

[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]

Reduce the numbers with G.C.F 2

[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]

Multiply the numbers

[tex] = 56 + 4 \times {4}^{2} [/tex]

Calculate the product

[tex] = 56 + {4}^{3} [/tex]

Evaluate the power

[tex] = 56 + 64[/tex]

Add the numbers

[tex] = 120[/tex]

Hope this helps..

best regards!!