Simplify the following exponential expression.
14405c4
- 166c-14

If we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.

Given that principal amount is $500 , years are 6 and rate of interest be 7%.

We are required to find the amount that we have to pay after 6 years if we borrow $500.

Compound interest is the interest that is calculated on the principal plus the accumulated interest at that point of time.

Sum after compounding is given as under:

S=P[tex](1+R)^{N}[/tex]

So we have to just put the values to find the money that we have to pay after 6 years.

S=500[tex](1+0.07)^{6}[/tex]

=500[tex](1.07)^{6}[/tex]

=500*1.5

=$750

Hence if we borrowed $500 for 6 years at a rate of 7% interest then we will have to pay approximately $750 after 6 years.

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Answer

speed : metres per second (a)

perimeter : meters (b)

volume : cubic centimetres (d)

area : square metres (c)

Answer:

A. $1.75 + $0.25x ≤ $15

Step-by-step explanation:

This is because if Eddie has 15 dollars, he can only use 15 dollars or less. So in this case, the inequality would have to be less than or equal to 15 dollars.  

Eddie travel $1.75 + $0.25x ≤ $15 miles when he has $15 to spend.

Option A is the correct option.

Here,

Amount of flat fee of taxi cab = $1.75

Amount of charge for each miles = $0.25

The amount Eddie has to spent = $15

We have to find inequality relationship.

What is inequality?

The relationship between two values that are not equal is defined by inequalities.

Now,

Amount of flat fee of taxi cab = $1.75

Amount of charge for each miles = $0.25

The amount Eddie has to spent = $15

Let Eddie travel x miles.

Therefore, the total charge of taxi cab = $1.75 + 0.25x

And this amount should not exceed the $15 as it is the only amount Eddie has.

Hence the inequality relationship be,

$1.75 + 0.25x ≤ $15.

Option A is the correct option.

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Answer:

The correct option is;

11

Step-by-step explanation:

The incenter is the point where the interior angle bisectors of the triangle meet, hence the interior angles are each bisected into two by the segments DA, EA, and FA respectively

Given that point A is the incenter of ΔDEF, we have;

∠FDE = ∠XDY is bisected by DA which gives ∠XDA = ∠YDA

∠LDA = ∠XDA = 27

∠MDA = ∠YDA = 3··n - 6

Therefore, 27 = 3·n - 6

3·n = 27 + 6 = 33

n = 33/3 = 11°

Answer:

11

Step-by-step explanation:

edge2020

Answer: See below

Step-by-step explanation:

When you see that something is to the power of a negative number, it is another way of saying 1 over.

[tex](2x-2)^-^3=\frac{1}{(2x-2)^3} =\frac{1}{(2x-2)(4x^2-8x+4)} =\frac{1}{8x^3-8x^2+8x-8}[/tex]

Answer:

#14) x is 95 (155-180= 25, 180-25-60= 95)

#19) my best guess is 4 (DE=7 -> AB=11, a 4 unit increase)

Answer:

≈93.6

Step-by-step explanation:

percent right = answers right/ anwers wrong

Answers right= 47-3=44

%=44/47

≈93.6

Answer:

C

Step-by-step explanation:

PLATO

So, sin E=0.5. Therefore, option C is the correct answer.

Given that, AB║DE and sinA= 0.5.

We need to find the value of sin E.

The value of sinθ must always be between −1 and 1. So the domain of f(x) = sinθ contains all the real numbers, but the range is −1 ≤ sin x ≤ 1. We can also see that the function repeats itself every 360°.

Now, sinA = 0.5

⇒∠A=30°

∠A=∠E=30° (∵∠A and ∠E are alternate angles)

Therefore, option C is the correct answer.

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Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

100.48

Step-by-step explanation:

Using the formula : 2pi times the radius, I can plug the radius in and find the circumference. 2 times pi is 6.28, and the radius is 16. 6.28 times 16 =  100.48.

Answer:

60

Step-by-step explanation:

360-95-120-85=60

Answer:

Yes, she can.

Step-by-step explanation:

We have to find the surface area of the footrest and see if it greater than or less than 1 square yard.

The surface area of a rectangular prism is given as:

A=2(wl+hl+hw)

where w = width, l = length, h = height

The footrest is 15 inches by 7 inches by 9 inches. Its surface area is:

A = 2[(7 * 15) + (9 * 15) + (9 * 7)]

A = 2[105 + 135 + 63]

A = 2 * 303 = 606 square inches

1 square inch = 0.000771605 square yards

=> 606 square inches = 606 * 0.000771605 = 0.468 square yards

Since the surface area of the prism is less than 1 square yard, she can completely cover the footrest with the fabric.

Answer:

Step-by-step explanation:

If you substitute x = -4 in the equation, you should get the y value as 3

y = 5x + 21

 = 5* -4 + 21

 = -20 + 21

y = -1 ≠ 3

So, (-4, 3) is not a solution

Answer: RS

Step-by-step explanation:

A greater angle of a triangle is opposite a greater side. If angle Q is greater than angle R, then side RS is greater than side QS.

Because Q is the larger angle in the triangle, Then RS is the longest side.

Answer:

The answer to number one is 11√17

The answer to number two is 4

Step-by-step explanation:

In number one: once you get both radicands to be equal, then you can add them. Like of it like 3x+2x. The x’s are like terms, so you can add them together.

In number two: the √5 on the top and bottom cancel out. This leaves 12/3 which is equal to 4.

Answer:

B 1/7^2

D 7^-10 / 7^-8

Step-by-step explanation:

7^-2

We know that a^-2 = 1/a^2

1/7^2 = 1/49

We also know that anything with a power of 2 in the denominator is good

7^-8 / 7^-10 = 7^2  

7^-10 / 7^-8 = 7^-2 = 1/7^2 = 1/69  that is the second answer

Answer:

Step-by-step explanation:

Answers C and D are correct.  

Note that in C we have    7^(-8)

                                         ---------- ,  

                                          7^(-10)

which is equivalent to 7^(-8 + 10), or 7^2, or 49.

Answer:

Its the first one

Step-by-step explanation:

10 and x is Greater than -2

Answer:

ED ≈ 2.6 units

Step-by-step explanation:

Using the Sine rule in Δ DEF

[tex]\frac{FD}{sin115}[/tex] = [tex]\frac{ED}{sin20}[/tex]

[tex]\frac{6.95}{sin115}[/tex] = [tex]\frac{ED}{sin20}[/tex] ( cross- multiply )

ED sin115° = 6.95 sin20° ( divide both sides by sin115° )

ED = [tex]\frac{6.95sin20}{sin115}[/tex] ≈ 2.6 ( to the nearest tenth )

Answer:

the answer is 15:75

Step-by-step explanation:

(1+5)=6

£90/6=15

So, (1×15):(5×15)

=15:75

Answer:

1/8÷7

Step-by-step explanation:

I think

Answer:

The first one

Step-by-step explanation:

The first simbol means that job is part of the Books of the Old Testament which is true, because the Book of Job it is in the Old Testament

Answer:

[tex]7n-6, \: 4n+8[/tex]

Step-by-step explanation:

[tex]+7[/tex] difference.

So it becomes [tex]7n[/tex].

[tex]7(1)+c=1[/tex]

[tex]c=-6[/tex]

Therefore, the nth term becomes:

[tex]7n-6[/tex]

[tex]+4[/tex] difference.

So it becomes [tex]4n[/tex].

[tex]4(1)+c=12[/tex]

[tex]c=8[/tex]

Therefore, the nth term becomes:

[tex]4n+8[/tex]

Answer:

a) 7n-6

b) 4n+8

Explanation:

a) 7 times tables but take away 6 for the start

b) 4 times tables but add 8 for the start

Answer:

Each Cup has 3/8

Step-by-step explanation:

Divide

Answer:

(3x^3 - 4y^3) ( 3x^3 + 4y^3)

Step-by-step explanation:

9x^6 – 16 y^6

Rewriting as

(3x^3) ^2 - ( 4y^3) ^2

This is the difference of squares a^2 - b^2 = (a-b)(a+b)

(3x^3 - 4y^3) ( 3x^3 + 4y^3)

Answer:

(3x^3 - 4y^3) ( 3x^3 + 4y^3)

Answer: (b - 4)(b - 3); b = 4 and 3

Step-by-step explanation:

ima assume these are exponents since you didnt care to correctly write the equation.

What two numbers multiply to equal 12, but add to equal -7? That's -4 and -3

So the factored form of this trinomial is (b - 4)(b - 3) = 0. Make each of these expressions equal to 0 in order to get your answer.

Answer:

Step-by-step explanation:

[tex]a^{-m}=(\frac{1}{a})^{m}\\\\\\1)7^{-2}=(\frac{1}{7})^{2}\\\\\\2)(\frac{2}{3})^{-3}=(\frac{1}{\frac{2}{3}})^{3}\\\\=(\frac{3}{2})^{3}[/tex]

Answer:

1) D.

2) A

Step-by-step Explanation:

1) [tex]7^{-2}[/tex]

= [tex](\frac{1}{7})^2[/tex]

2) [tex](\frac{2}{3})^{-3}[/tex]

= [tex](\frac{3}{2})^{3}[/tex]

Answer:

Step-by-step explanation:

You have a vertex coordinate and 2 points. In order to write the equation for that parabola, you only need the vertex and one point. We will fill in the following work form of the parabola:

[tex]y=a(x-h)^2+k[/tex] , where h and k are from the vertex and x and y are from the point. Filling in:

[tex]12=a(8-5)^2+3[/tex] and

[tex]12=a(3)^2+3[/tex] and

[tex]12=9a+3[/tex] and

9 = 9a s0

a = 1.

Now we can write the equation, filling in a, the only unknown we had, which we now know is 1:

[tex]y=1(x-5)^2+3[/tex]

Answer:

y =  1 (x +  -5 )2 + 3

Step-by-step explanation:

Answer: 2/3xy^-2z

Step-by-step explanation:

18/27 = 2/3

x^2 / x = x

y / y^3 = y^-2

z isn’t changed

Put the variables together after dividing and you get 2/3xy^-2z.

Step-by-step explanation:

do you mean like this?

18x²y/27xy³z =

if yes the answer is like this

18/27 = 2/3

x²/x = x

y/y³ = 1/y²

1/z = 1/z

multiply all and that's the answer

⅔ * x * 1/y² * 1/z =

[tex] \frac{2x}{3 {y}^{2} z} [/tex]

Answer:

16:24 is the answer

Hope it helps:)

Step-by-step explanation:

The initial number of cards were

1x:1x

(Equal red cards and black cards)

So, total of 48 and..

24 red cards

24 black cards

Now, since 8 red cards are removed we have,

24-8= 16 red cards

and 24 black cards

So the ratio of red to black is--

16:24

= 2:3 ( i divided both with 8 to simplify )

Pack 48                          48/2 =24

Red= 24                      24/24 : 24 / 24

Black = 24                            1:1

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

Pack 48                        48/2 = 24    

Red= 16                     24 / 16 : 24 / 24

Black= 24                    1,5 : 1

There's 1,5 black cards for each red card