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3 years ago

Solve for x. Round to two decimal places if necessary.

Mathematics

1 answer:

Alik [6]3 years ago

4 0

Answer:

Length of JK is 68.27 units.

Step-by-step explanation:

By applying geometric mean theorem (leg theorem) in the triangle attached,

$\frac{KL}{KM}= \frac{JK}{KL}$

(KL)² = (KM)(JK)

(32)² = (15)(x)

x = $\frac{1024}{15}$

x = 68.2666

x ≈ 68.27

Therefore, length of JK is 68.27 units.

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The equation 1.5r+15=2.25r1.5r+15=2.25r represents the number rr of movies you must rent to spend the same amount at each movie

Lelu [443]

1.5r+15=2.25r
Combine like terms: 1.5r+15-1.5r=2.25r-1.5r
15=0.75r
Get the unknown alone: 15/.75=.75/.75r
20=r or r=20 :)

7 0

3 years ago

Which length is equivalent to 12 yards?

elena-s [515]

Answer:

Step-by-step explanation:

there are 3 ft in a yard, so to find how many yards you multiply 3 time 12, which equals 36.

5 0

3 years ago

Read 2 more answers

A bacteria sample can be modeled by the function f(x) - 350(1.20) which gives the number of bacteria in the sample at the end of

marissa [1.9K]

Answer: A) The initial number of bacteria is 350.

Step-by-step explanation:

Exponential growth equation: $f(x)=A(1+r)^x$ , where A=Initial value, r= growth rate. (i)

Given: A bacteria sample can be modeled by the function $f(x) = 350(1.20)$ which gives the number of bacteria in the sample at the end of x days.

Here, $f(x)=350(1+0.20)$

Compare this equation to (i) , we get A = 350 and r= 0.20 = 20% (growth rate)

So, the best interpretation of one of the values in this function are:

A) The initial number of bacteria is 350.

3 0

3 years ago

A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t

Solnce55 [7]

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

$h=-16t^2+200t$

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

$350=-16t^2+200t$

The last is a quadratic equation, which can be put in the form $at^2+bt+c=0$ and solved applying the formula:

$t=\frac{-b+-\sqrt{b^2-4ac} }{2a}$

So, let's put the equation on the form $at^2+bt+c=0$ adding $16t^2$ and subtracting $200t$ to each side of the equation; the result is:

$16t^2-200t+350=0$

So, we note that a=16, b=-200, and c=350.

Then,

$t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10$

$t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40$

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

4 0

3 years ago

Determina si 2018 es un termino de la siguiente progresion aritmetica 17,46,75,104,133,....

Kitty [74]

2018 is the 70th term of the progression.

Explanation
We start out finding the common difference of the progression:
46-17 = 29

Now we write the explicit formula for the sequence. It is of the form
$a_n=a_1+d(n-1)
\\
a_n=17+29(n-1)$

We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:

2018=17+29(n-1)

Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29

Combine like terms:
2018=29n-12

Add 12 to both sides:
2018+12=29n-12+12
2030=29n

Divide both sides by 29:
2030/29=29n/29
70=n

Since n=70, this means 2018 is the 70th term of the sequence.

8 0

4 years ago