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Agata [3.3K]
3 years ago
7

Is this the correct answer?

Mathematics
1 answer:
Shtirlitz [24]3 years ago
5 0

Answer:

yes

Step-by-step explanation:

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If Lana deposits $500 into a savings account that gains simple interest at
Oksana_A [137]

Answer:

10 years

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year,

then, solving our equation

t = 100 / ( 500 × 0.02 ) = 10

t = 10 years

The time required to

accumulate simple interest of $ 100.00

from a principal of $ 500.00

at an interest rate of 2% per year

is 10 years.

3 0
3 years ago
Log(x-2)+log2=2logy<br>log(x-3y+3)=0​
In-s [12.5K]

Answer:

<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right

===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}

\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac

y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D

\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D

4 0
3 years ago
5-7
uranmaximum [27]

Answer:

the third option

Step-by-step explanation:

what does that mean ?

to "rationalize" it is to transform it into a rational number (that is a number that can be described as a/b, and is not an endless sequence of digits after the decimal point without a repeating pattern).

a square root of a not square number is irrational (not rational).

so, what this question is asking us to get rid of the square root part in the denominator (the bottom part).

for this we need to multiply to and bottom with the same expression (to keep the whole value of the quotient the same) that, when multiplied at the bottom, eliminates the square root.

what can I multiply a square root with to eliminate the square root ? the square root again - we are squaring the square root.

so, what works for 9 - sqrt(14) as factor ?

we cannot just square this as

(9- sqrt(14))² = 81 -2sqrt(14) + 14

we still have the square root included.

but remember the little trick :

(a+b)(a-b) = a² - b²

without any mixed elements.

so, we need to multiply (9-sqrt(14)) by (9+sqrt(14)) to get

81-14 = 67 which is a rational number.

therefore, the third answer option is correct.

7 0
3 years ago
Graph the linear function r(x)=2
wlad13 [49]

It's a linear function with a slope 0.

It's a horizontal line (look at the picture).

4 0
3 years ago
If the side length of a square is 4 inches, it’s area is how many square inches and it’s perimeter is how many inches
riadik2000 [5.3K]

Answer:

The area is 16 inches squared and the perimeter is also 16 inches

Step-by-step explanation:

To find the area, you must multiply the length by the width. Since this is a square, you have to multiply one adjacent side by the other. For perimeter, you can either multiply one side by 4 or add all 4 sides.

6 0
2 years ago
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