Solve the equation for the given variable a/2 + 4 = 6

Express 3^2 = x as a logarithmic equation.

Dennis_Churaev [7]

Remember
$a^b=c$ translates to $log_a(c)=b$

so

$3^2=x$ translates to $log_3(x)=2$

5 0

3 years ago

I’ve been stuck on question 1 for a while, can you guys help?

MakcuM [25]

Answer:

$h=20$ **

**The picture is not accurate for this problem.

Step-by-step explanation:

I would use Pythagorean Theorem to setup two equations since there are two triangles with no angle information.

Let $BC=x+(99-x)$ where $x$ is equal to the first partition of $BC$ (reading from left to right) and $(99-x)$ is equal to the second partition of $BC$ (reading from left to right).

We have the following system to solve:

$20^2=h^2+x^2$

$101^2=h^2+(99-x)^2$

I will use elimination to first solve for $x$ .

Subtract the equations:

$20^2-101^2=x^2-(99-x)^2$

Factor both sides using $a^2-b^2=(a-b)(a+b)$ :

$(20-101)(20+101)=(x-(99-x))(x+(99-x))$

Simplify inside the $($ $)$ .

$(-81)(121)=(2x-99)(99)$

Divide both sides by 9:

$(-9)(121)=(2x-99)(11)$

Divide both sides by 11:

$(-9)(11)=(2x-99)(1)$

Simplify both sides:

$-99=2x-99$

Add 99 on both sides:

$0=2x$

Divide both sides by 2:

$x=0$

Now go to either equation we had in the beginning to find $h$ .

$20^2=h^2+x^2$ with $x=0$

$20^2=h^2$

$20=h$

4 0

3 years ago

What does the consumer price index measure?

juin [17]

The consumer price index or the CPI measures the average change over time in the prices paid by a customer <span>for a market basket of consumer goods and services.</span>

4 0

4 years ago

Read 2 more answers

sarah, natasha and richard share some sweets in the ratio 5:2:4. sarah gets 60 sweets. how many did richard get?

Sindrei [870]

Answer:

48 sweets

Step-by-step explanation:

5:2:4

Sarah: 5

Natasha:2

Richard:4

To find out how many sweets Richard got, we need to use 60 as the lcm. Since, we have a definite constant of 60 we need to divide it by the presiding ratio.

60/5 = 12

That means for a ratio of 1, everyone in the group recieves 12.

Now, we plug it in for each of the members.

5x = Sarah

2x = Natasha

4x = Richard

Sarah = 60 sweets

Natasha = 24 sweets

Richard = 48 sweets

6 0

3 years ago

Write an equation in slope-intercept form for the line passing through the pair of points. (–1, 2), (4, –3)

dybincka [34]

Answer:

y = - x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)

m = $\frac{-3-2}{4+1}$ = $\frac{-5}{5}$ = -1, hence

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, 2), then

2 = 1 + c ⇒ c = 2 - 1 = 1

y = - x + 1 ← equation in slope- intercept form

8 0

3 years ago