Solve : (i) 5x+3/4 - 2x-4/3 = 5 (ii) 3(x+5) - 2(3x-1) = 15

Answer:

Option A) A = 100(1.005)^12t

Step-by-step explanation:

The formula for Total Amount obtained using compound interest is given as:

A = P( 1 + r/n) ^nt

Where

A = Total amount received or obtained after investing

P = Principal or Initial Amount invested

r = interest rate

n = rate or number of times the interest is compounded

t = time in years.

In the question we obtained this values

P = $100

r = 6% = 0.06

n = compounded monthly, we have 12 months in a year, hence, n = 12

t = t

Using the compound interest formula for Amount A,

A = P( 1 + r/n) ^nt

A = 100(1 + 0.06/12)^12 × t

A = 100(1 + 0.005)^12t

A = 100(1.005)^12t

Therefore, the value of Mari's Investment if the interest is compounded monthly is

A = 100(1.005)^12t

Hence, Option A is correct.

Answer:

Option (D) : 13

Step-by-step explanation:

Mode is the observation which occurred the most number of time.

Therefore, mode = 13

Answer:

-5/24

Step-by-step explanation:

get a common denominator = 24

-14/24 + 9/24 = -5/24

Answer:-5 /24 ez

Step-by-step explanation:

[tex] 5 day= 120h \\ 600m = 10h \\ 120 + 10 + 4 = 134h[/tex]

Answer:

Step-by-step explanation:

Volume of the can is expressed as Length *Breadth* Height.

If the area of the can base is Length * Breadth

Volume of the can = area of the base of the can * Height

Given parameters

Volume of the can V = 3416.32cm³

Height of the can h = 17cm

Required

Area of the base of the can

Substituting the given parameters into the formula we have;

V = Ah

A = V//h

A = 3416.32/17

A = 200.96cm²

Hence, the area of the base of the can is 200.96cm²

Answer:

approximately 12.04 units

Step-by-step explanation:

We'll use the Pythagorean Theorem to solve this problem.

There are two points here.  The horizontal distance between them is 8 units and the vertical distance is 9.

According to the Pythagorean Theorem (or the Distance Formula), the distance between the two points is

d = √(8^2 + 9^2) = √(64 + 81) = √145 units, or approximately 12.04 units.

Total weight required is half pound, so let the amount of cashews be [tex] a[/tex] , and amount of peanuts be $b$

$\therefore a+b=0.5$ (1)

And we want this to cost $2.80$

Cost of $a$ pound of cashews will be $5.50\times a$ and cost of $b$ pound peanuts will be $2.30\times b$

$\therefore 5.5a+2.3b=2.8$ (2)

Substitute $a=0.5-b$ from equation (1) in equation (2)

$5.5(0.5-b)+2.3b=2.8$

$\implies -3.2b=2.8+5.5\times0.5 $

$\implies -3.2b=0.05$

$b$ comes out to be negative. That means there's no solution with the given conditions.

I checked once , I don't think there's any mistake. Can someone else verify too?

EDIT

I verified all the given options from calculator, and no option gives 2.80

Step-by-step explanation:

Let's start by finding the area of figure 1

The square:

15cm×15cm=225cm²

Then we're going to find the area of figure 2

it's a rectangle (A=L×W)

L=60cm-15cm(because those cm have been cut off)=45cm

W=40cm

Area=45cm×40cm

=1800cm²

Then we add up the sum

Area of 1+Area of 2

=225cm²+1800cm²

=2025cm²

Answer:

140 cm is the perimeter of the unshaded shape.

Step-by-step explanation:

Perimeter of the rectangle in whole = 2l + 2w

Where length is 60 cm and width is 40 cm.

P = 2 × 60 + 2 × 40

= 120 + 80

= 200 cm

To find the perimeter of the unshaded square = 4l

Where the length is 15 cm.

P = 4× 15

= 60 cm

To find the perimeter of the shaded shape = Perimeter of rectangle - Perimeter of unshaded square.

P = 200 - 60

= 140 cm

140 cm is the perimeter of the unshaded shape.

Answer:

17.25 miles

1 hour, 56 minutes, and 20 seconds.

4 hours, 47 minutes, and 38 seconds.

Step-by-step explanation:

Part I:

For his three cycling sessions, he had traveled for 25.8 miles, 17.25 miles, and 27.42 miles.

The shortest distance he cycled is 17.25 miles.

Part II:

For his three cycling sessions, he spent: 1) 1 hour, 56 minutes, and 20 seconds, 2) 1 hour, 1 minute, and 13 seconds, and 3) 1 hour 50 minutes and 5 seconds.

The longest time he cycled for was 1 hour, 56 minutes, and 20 seconds.

Part III:

Lance's total cycling time is all the times added together. Therefore:

[tex]1\text{ hr} +1\text{ hr} +1\text{ hr} +56\text{ min} +1\text{ min}+50\text{ min} +20\text{ sec}+13\text{ sec} +5\text{ sec} \\\\=3\text{ hr} +107\text{ min}+38\text{ sec} \\\\=4\text{ hours, }47\text{ minutes}\text{ and 38 seconds}[/tex]

Answer:

i) 17.25 miles.

ii) 1 hrs :56 mins :20 secs

iii) 4 hrs :47 mins: 38 secs total.

Answer:

12

Step-by-step explanation:

Because you add 8 to the 40 which is 48 then divide equaling 12

Answer:

12

Step-by-step explanation:

40+8=48

48/4=12

Answer:

Step-by-step explanation:

y = -2x - 5

perp. slope: 1/2

y + 2 = 1/2(x + 1)

y + 4/2 = 1/2x + 1/2

y = 1/2x - 3/2

Answer:

239 ft².

Step-by-step explanation:

Let P represent the price for tiling.

Let S represent the size of the room.

From the question,

Price (P) varies directly as the size (S) i.e

P & S

P = KS

Where K is the constant of proportionality.

Next, we shall determine the value of K as follow

Price (P) = $ 4224

Size (S) = 264 ft²

Constant of proportionality (K) =?

P = KS

4224 = K × 264

Divide both side by 264

K = 4224/264

K = 16

Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.

This is illustrated below:

Price (P) = $ 3824

Constant of proportionality (K) = 16

Size (S) =?

P = KS

3824 = 16 × S

Divide both side by 16

S = 3824/16

S = 239 ft²

Therefore, the size of the kitchen is 239 ft².

Answer:

x= 6 degrees

Step-by-step explanation:

x+x+54 = 90

2x+54 = 90

x= 90- 54 /2

x =6

Answer:

x = 6

Step-by-step explanation:

90 - 54 = 36

x + 5x = 6x

36 + 6x = 90

90 - 36 = 6x

36/6x = 6

x = 6

Answer:

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Step-by-step explanation:

We need to find the value of expression [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}[/tex].

Firstly solving the second term as :

[tex](2-\dfrac{3}{8})=\dfrac{16-3}{8}=\dfrac{13}{8}[/tex]

Now the above expression becomes,

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}\\=\dfrac{-3}{2}-\dfrac{13}{8}+\dfrac{3}{2}[/tex]

-3/2 and +3/2 equals 0.

It means that, [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Answer:

The correct answer is B.

Step-by-step explanation:The entrance fee ($18) and the cost per ball ($0.08B) added together should equal greater or equal to $75 in order to receive $10 off.

Answer:

m=7

Step-by-step explanation:

subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.

Answer: m=7

Step-by-step explanation:

[tex]5m+35=70[/tex]

subtract 35 on both sides

[tex]5m+35-35=70-35[/tex]

[tex]5m=35[/tex]

divide 5 on both sides

[tex]35/5=7[/tex]

[tex]m=7[/tex]

Answer:

Amount saved by making a cash payment is $24.6

Step-by-step explanation:

We start by calculating the amount to be paid if payment was by installments.

We are told that there would be a down payment of $25 and $15 every month for 12 months.

So total installment payment would be;

$25 + 12($15) = $25 + $180 = $205

Now let’s try and figure out the cash payment

For the cash payment, we have 12% less than installment payment.

Kindly note that 12% is same as 12/100 = 0.12

Thus, 12% less payment would be;

205-0.12(205) = 205 - 24.6 = $180.4

Thus, the amount saved if payment was cash would be;

$205 - $180.4 = $24.6

Answer:

Step-by-step explanation:

[tex]3.4-2.8d+2.8d-1.3\\\\\mathrm{Add\:similar\:elements:}\:-2.8d+2.8d=0\\\\=3.4-1.3\\\\\mathrm{Subtract\:the\:numbers:}\:3.4-1.3\\\\=2.1[/tex]

Answer: B) different y intercepts; same end behavior

=======================================================

Explanation:

The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.

The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function

g(x) = 4(1/4)^x + 2

g(0) = 4(1/4)^0 + 2

g(0) = 6

So we can see the y intercepts are different.

----------

However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.

In terms of symbols, [tex]x \to -\infty, y \to \infty[/tex]

----------

For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.

In terms of symbols, [tex]x \to \infty, y \to 2[/tex]

Answer:

No! They are not proportional!

Step-by-step explanation:

Proportional prices to the length means that

(price 1/length 1)=(price 2/length 2)=(price 3/length 3)

Even by plugging in the numbers yourself to double check my numbers, and getting and answer for each ratio, it is clear that they are not proportional.

Answer:

The ratio of screen length to price in the first row is 16/160, which simplifies to 1/10.

The ratio of screen length to price in the second row is 20/180, which simplifies to 1/9.

The ratio of screen length to price in the third row is 24/200, which simplifies to 3/25.

Because 16/160 doesn't = 20/180 doesn't = 24/200, the ratios are not equivalent. This is not a proportional relationship.

Answer:

One thousand two hundred and forty five.

Hope this helps! （づ￣3￣）づ╭❤～

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is not properly written. Here is the correct question.

You are the owner of Decorama Flooring. Tod and Claudia have asked you to give an estimate for tiling four rooms of their house. The living room is 15 feet*23 feet, dinning room is 12ft*18ft, the kitchen is 9ft*11 ft and the study room is 10ft*12 ft how many square ft of tiles are required for each room. (multiply length by the width).

We must understand that a floor tile is rectangular in nature.

Area of a rectangle = Length * width

To get the amount of square feet required for each room, we must multiply the length and width of each of the rooms together as shown.

For the living room;

Length = 15 feet and Width = 23 feet

Amount of square feet of tiles needed for the living room = 15feet * 23 feet

= 345 ft²

For the dining room;

Length = 12 feet and Width = 18 feet

Amount of square feet of tiles needed for the dining room = 12feet * 18 feet

= 216 ft²

For the kitchen;

Length = 9 feet and Width = 11 feet

Amount of square feet of tiles needed for the kitchen = 11feet *9feet

= 99 ft²

For the study room;

Length = 10 feet and Width = 12 feet

Amount of square feet of tiles needed for the study room = 10feet * 12 feet

= 120 ft²

Step-by-step explanation:

[tex]2 + 8(x + 2) = 52 [/tex]

[tex]2 + 8x + 16 = 52[/tex]

[tex]8x + 18 = 52[/tex]

[tex]8x = 52 - 18[/tex]

[tex]8x = 32[/tex]

[tex]x = \frac{34}{8} [/tex]

[tex]x = 4.25[/tex]

Hope it helps u

Answer: terminating

Step-by-step explanation:

Answer:

7.2 is a terminating decimal.

Step-by-step explanation:

Terminating decimals are decimals that have an end point. The decimal does not continue to go on and on with numbers but, it stops at one number which makes it terminating.

Repeating decimals are decimals that go on and on with the same number or same patterns of numbers.

So, since 7.2 has an endpoint, then it is a terminating decimal.

Answer:

I think the answer is both

Answer

hope this helps

Answer:

A, B, E

Step-by-step explanation:

Solve all equations for x. The equivalent equations are the equations that have the same solution.

A   2 + x = 5; x = 3

B   x + 1 = 4; x = 3

C   9 + x = 6; x = -3

D   x + (-4) = 7; x = 11

E   -5 + x = -2; x = 3

Equivalent equations: A, B, E

Answer:

Last statement is the true one: AH congruent with AB

Step-by-step explanation:

Since the FG is congruent with KC, then the central angles defined by this chords are the same. and since the segments AH and AB are perpendicular to the segments GF and KC respectively (intersecting them at exactly half of their length), they form right angle triangles of which the hypotenuse is the actual radius of the circle, one of the legs of these triangles is half of the segments GF and KC of equal length. Then the third legs of those right angle triangles (AH and AB) must be equal as well.

Answer:

4.5

Step-by-step explanation:

Hello, please consider the following.

First of all, let's assume that A is different from 0.

[tex]x^2+8x+4\\\\\text{It means that the sum of the zeroes is -8 and the product is 4}\\\\Ax^2+Bx+1=A(x^2+\dfrac{B}{A}x+\dfrac{1}{A})\\\\\text{So the sum of the zeroes is } -\dfrac{B}{A} \text{ and the product is }\dfrac{1}{A}\\\\\text{It comes.}\\\\-\dfrac{B}{A}=-8 <=> \dfrac{B}{A}=8\\\\\dfrac{1}{A}=4[/tex]

So,

[tex]A=\dfrac{1}{4}\\\\B=\dfrac{8}{4}=2\\\\A+B=\dfrac{1+8}{2}=\dfrac{9}{2}=4.5[/tex]

Thank you.