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2 years ago

Rationalize the denominator and simplify. 5/4-√3

1 answer:

4 0

I assume the denominator is (4-√3)
Multiple both top and bottom by (4+√3)
[5(4+√3)]/[(4-√3)(4+√3)]
=[20+5√3]/[4²-(√3)²]
=[20+5√3]/13

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Use the common ratio to find the next term of the geometric sequence. Type a numerical answer in the space provided.

prisoha [69]

Answer:

Step-by-step explanation:

the common ratio is 1/2 so you do 30(1/2)

30(1/2)=15

5 0

2 years ago

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the

Lera25 [3.4K]

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given $h=1+2s$ where $h$ is the hypotenuse and $s$ is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with $h$ , "is" with $=$ , "1 foot more than" with $1+$ and finally "twice the length of the shorter leg" with $2s$ .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with $L$ .

I'm going to replace "is" with $=$ .

I'm going to replace "7 feet longer than the shorter leg" with $7+s$ .

So we have the equation $L=7+s$ .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: $s^2+L^2=h^2$ .

Let's make some substitutions from above:

$s^2+(7+s)^2=(1+2s)^2$

Let's expand the powers using:

$(a+b)^2=a^2+2ab+b^2$

Applying this now:

$s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)$

$s^2+49+14s+s^2=1+4s+4s^2$

Combine like terms on right hand side:

$2s^2+49+14s=1+4s+4s^2$

Subtract everything on left hand side to get 0 on that side:

$0=(1-49)+(4s-14s)+(4s^2-2s^2)$

Simplify:

$0=(-48)+(-10s)+(2s^2)$

Reorder into standard form for a quadratic:

$0=2s^2-10s-48$

Every term is even and therefore divisible by 2. I will divide both sides by 2:

$0=s^2-5s-24$

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

$0=(s-8)(s+3)$

This implies that either $s-8=0$ os $s+3=0$ .

The first equation can be solved by adding 8 on both sides: $s=8$ .

The second equation can be solved by subtracting 3 on both sides: $s=-3$ .

The only solution that makes sense for $s$ is 8 since it can't the shorter length cannot be a negative number.

$s=8$

$L=7+s=7+8=15$

$h=1+2s=1+2(8)=1+16=17$

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

6 0

2 years ago

Marco wants to invest his savings in a bank for 3 years. He has borrowed £15,0000 to invest and receives offers from two banks.

azamat

Answer:

Marcos Should invest with the first bank

Step-by-step explanation:

Formula for finding compound interest is: A = p(1+\frac{r}{n})^{nt}

where

A = the future value of the investment

P = the principal investment amount (the initial deposit)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

If marcos choose to invest with the first bank

A = 15000(1+\frac{0.025}{12})^{12*3} = £16166.81

If he choose to invest with the second bank

His principal become 15570 in the first year because of the 3.8% offer from the bank and t becomes 2.

A = 15570(1+\frac{0.01}{12})^{12*2} = £15884.27

Comparing the future value of his investment from both bank, Marcos will get more interest from investing with the first bank.

5 0

2 years ago

Read 2 more answers

Solve for <br> please help!!

Snowcat [4.5K]

Answer:

x = 76°

Step-by-step explanation:

At point I

to get angle JID

angle JID + 107° = 180°. (angle on a straight line)

angle JID = 180° - 107°

angle JID = 73°

for Triangle JiD

angle DJI + 31° + 73° = 180° (Sum of angles in a triangle)

angle DJI = 180 - 104 = 76°

angle FJI = 31 + 73 =104°. ( Sum of two interior angles in a triangle is equal to one exterior angle)

Hence,

x° + 104° = 180° (angle on a straight line)

x = 76°

7 0

2 years ago

If the big hand of the clock rotates through 90 degrees in 15

ehidna [41]

Answer:

270 degrees

Step-by-step explanation:

45/15 is 3 and 90 times 3 is 270

4 0

2 years ago