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2 years ago

Last one was 5(x + y)

Mathematics

1 answer:

Oksana_A [137]2 years ago

5 0

Answer:

1. 2x - 5

2. 5(x + y)

3. (5 - x)²

Step-by-step explanation:

1. Five less than the twice the number

Let the number be 'x'. 5 less than twice the number = 2x - 5

2. Five times the sum of two numbers

Let the two numbers be 'x' and 'y'. Then the notation would be: 5(x + y)

3. The difference of 5 and a number, squared

Let the number be 'x'. The mathematical expression for the above statement would be: (5 - x)².

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Find the slope of the line that passes through the points (1, 1) and (7, 5).

Nata [24]

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=5-1/7-1

m=4/6

m= 2/3

The slope is 2/3

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2 years ago

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You have $5600. The best interest rate you can find is 3%

EleoNora [17]

Answer:

18 years

Step-by-step explanation:

The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by

$A = P(1 + \frac{r}{n})^{nt}$

Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03

We can rearrange the above equation to:

$\frac{A}{P} = (1 + \frac{r}{n})^{nt}$

Taking logs on both sides

$log(\frac{A}{P}) = log(1 + \frac{r}{n})^{nt}$

This gives

$log(\frac{A}{P}) =nt \times log(1 + \frac{r}{n})\\So,\\nt = \frac{log(\frac{A}{P})}{ log(1 + \frac{r}{n})}$

In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075

1 + r/n = 1+0.0075 = 1.0075

4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72

t = 72/4 = 18 years

4 0

1 year ago

What is 1/20 multiplied by 23 as a mixed number

N76 [4]

Answer:

1 3/20

Step-by-step explanation:

6 0

2 years ago

HELLOOOO HELP PLEASE

MA_775_DIABLO [31]

Answer:

$2*log(x)+log(y)$

Step-by-step explanation:

So, there are two logarithmic identities you're going to need to know.

<em>Logarithm of a power</em>:

$log_ba^c=c*log_ba$

So to provide a quick proof and intuition as to why this works, let's consider the following logarithm: $log_ba=x\implies b^x=a$

Now if we raise both sides to the power of c, we get the following equation: $(b^x)^c=a^c$

Using the exponential identity: $(x^a)^c=x^{a*c}$

We get the equation: $b^{xc}=a^c$

If we convert this back into logarithmic form we get: $log_ba^c=x*c$

Since x was the basic logarithm we started with, we substitute it back in, to get the equation: $log_ba^c=c*log_ba$

Now the second logarithmic property you need to know is

<em>The Logarithm of a Product</em>:

$log_b{ac}=log_ba+log_bc$

Now for a quick proof, let's just say: $x=log_ba\text{ and }y=log_bc$

Now rewriting them both in exponential form, we get the equations:

$b^x=a\\b^y=c$

We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:

$b^x*b^y=a*c$

Using the exponential identity: $x^{a}*x^b=x^{a+b}$ , we can rewrite the equation as:

$b^{x+y}=ac$

taking the logarithm of both sides, we get:

$log_bac=x+y$

Since x and y are just the logarithms we started with, we can substitute them back in to get: $log_bac=log_ba+log_bc$

Now let's use these identities to rewrite the equation you gave

$log(x^2y)$

As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)

$log(x^2)+log(y)$

Now using the logarithm of a power to rewrite the log(x^2) we get:

$2*log(x)+log(y)$

3 0

1 year ago

Guests at an amusement park must be at least 54 inches tall to be able to ride the roller coaster. Which graph represents the se

Gre4nikov [31]

Given:

Guests at an amusement park must be at least 54 inches tall to be able to ride the roller coaster.

To find:

The graph that represents the set of heights that satisfy this requirement.

Solution:

Let x be the height required for the ride.

Guests must be at least 54 inches tall to be able to ride the roller coaster. It means required height is greater than or equal to 54.

$x\geq 54$

So, 54 and all values above 54 are in the solution set.

Since, 54 is included in the solution set, therefore there is a closed circle at 54. All values above 54 are in the solution set, so everything to the right of the circle is shaded.

Therefore, the correct option is C.

3 0

2 years ago

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