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Ede4ka [16]
3 years ago
13

Find two positive consecutive odd integers such that square of the smaller integer is 10 more than the larger integer

Mathematics
1 answer:
Otrada [13]3 years ago
3 0

Let 2n+1 be the smaller integer. The larger integer is then 2n+3, and we have

(2n+1)^2=10+(2n+3)\implies4n^2+4n+1=2n+13

\implies4n^2+2n-12=0

\implies2n^2+n-6=0

\implies(2n-3)(n+2)=0

\implies 2n-3=0\text{ or }n+2=0

\implies n=\dfrac32\text{ or }n=-2

We omit n=-2, since 2(-2)+1=-3 is negative.

Then for n=\dfrac32 we find 2\left(\dfrac32\right)+1=4, but this is not odd.

There are no consecutive odd integers that satisfy the given condition!

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The sides of an equilateral triangle are 8 units long.what is the length of the altitude of the triangle?
dedylja [7]

Answer:

Equilateral triangle implies each angle is 60 degree.

And any median is the altitude.

So, NT perpendicular LM, where T is the midpoint of [ML];

We use the Pythagorean Theorem in right triangle NTL ( NT = h; NL = a;

LT = a / 2 );

h² = a² - (a/2)² = a² - a²/4 = 4a²/4 - a²/4 = 3a²/4 ;

It follows that

h = √(3a²/4) = a√3/2 ≈ 0,866*a;

But, a = 8;

h ≈ 0,866 * 8 ≈ 6,928;

Step-by-step explanation:


6 0
4 years ago
Solve the equation 6=y-5 which step can you use to solve the equation 6+y-5
bazaltina [42]

Answer:

1.)6=y-5

On transposing y to L.H.S, we obtain

6+5=y

11=y

Step-by-step explanation:

Hope this helps you

If yes then do mark my answer as brainliest

3 0
3 years ago
What is 24.79 x 4,022 pls
lozanna [386]

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6 0
2 years ago
Read 2 more answers
What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 4?
ss7ja [257]

Answer:

B

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then multiply each of the coordinates by 4 , that is

A (0, 10 ) → A' (4(0), 4(10) ) → A' (0, 40 )

B (8, 6 ) → B' (4(8), 4(6) ) → B' (32, 24 )

C (4, 2 ) → C' (4(4), 4(2) ) → C' (16, 8 )

6 0
3 years ago
10.Adrienne is going to deposit $8,500 in an account that earns 2.5% interest for 360 months. How much more interest will she ea
suter [353]

Answer:

Difference= $3,090.15 in favor of compounded interest

Step-by-step explanation:

Giving the following information:

Present value (PV)= $8,500

Ineterest (i)= 0.025/12= 0.00208

Number of periods (n)= 360 months

<u>We will calculate the future value of each option and determine the difference:</u>

<u>Simple interest:</u>

FV= (PV*i*n) + PV

FV= (8,500*0.00208*360) + 8,500

FV= $14,864.8

<u>Compounded interest:</u>

FV= PV*(1+i)^n

FV= 8,500*(1.00208^360)

FV= $17,958.95

Difference= $3,090.15

6 0
2 years ago
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