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3 years ago

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A tree casts a shadow that is about 10 ft long. Javier, who is about 5 ft tall, is standing near the tree. Javier’s shadow is ab

out 4 ft long. What is the estimated height, t, of the tree?

1 answer:

Tju [1.3M]3 years ago

5 0

10 4 , so basically you cross multiply : 10x=20 .... 20 divided by 10 is 2 . x=2

___ = ___

5 x

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Factorise 2x^2 - 3x -2 < 0

Galina-37 [17]

Step 1: Factor $2 x^{2} - 3x -2$
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite $-3x$ as the sum of $x$ and $-4x$

$2 x^{2} +x-4x-2\ \textless \ 0$

Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.

</span> $x(2x+1)-2(2x+1)\ \textless \ 0$
<span>
Step 3: </span>Factor out the common term $2x+1$

$(2x+1)(x-2)\ \textless \ 0$

Step 4: Solve for $x$

1. Ask: When will $(2x+1)(x-2)$ equal zero?
2. Answer: When $2x + 1 = 0$ or $x-2=0$
3. <span>Solve each of the 2 equations above:

</span> $x=- \frac{1}{2} ,2$
<span>
Step 5: </span>From the values of $x$ <span>above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2

Step 6: P</span><span>ick a test point for each interval

</span>For the interval $x\ \textless \ - \frac{1}{2} 
$
Lets pick $x=-1.$ Then, $2(-1) ^{2} -3 * -1 -2 \ \textless \ 0$
After simplifying, we get $3\ \textless \ 0$ , Which is false.
Drop this interval.
<span>
For this interval $- \frac{1}{2} \ \textless \ x\ \textless \ 2$
Lets pick $x=0$ . Then, $2* 0^{2} - 3 * 0-2\ \textless \ 0$ . After simplifying, we get $-2\ \textless \ 0,$ which is true. Keep this <span>interval.

For the interval </span> $x\ \textgreater \ 2$

Lets pick $x = 3.$ Then, $2 * 3 ^{2} -3*3-2\ \textless \ 0.$ After simplifying, we get $7\ \textless \ 0$ , Which is false. Drop this interval.

.Step 7: Therefore,
$- \frac{1}{2} \ \textless \ x\ \textless \ 2$

Done! :)</span>

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3 years ago

Work out the size of angle x.

klemol [59]

Answer:

120°

Step-by-step explanation:

since 60° and x are alternate interior

you get this equation

60° + x = 180

subtract 60 from both sides

x = 120

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2 years ago

The local library charges 6 cents for each day a book is overdue plus a one-time record keeping fee of 19 cents. the function ta

Natasha2012 [34]

B. 241
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3 years ago

Evaluate f (x) = 3 (2)x for x=-1

kap26 [50]

The value of the function at x = -1 is 5

<h3>What is function?</h3>

Function can be defined as an expression, rule, or law that defines a relationship between one variable known as the independent variable and another called the dependent variable.

From the information given, we have that;

f (x) = 3 (2)x with x=-1

Now, let's substitute the value of x as - 1 in the function given;

f (x) = 3 (2)x

f (x) = 3 (2) -1

Expand the bracket;

f (x) = 6 - 1

f(x) = 5

Thus, the value of the function at x = -1 is 5

Learn more about functions here:

brainly.com/question/6561461

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Arte-miy333 [17]

My guess would be C but im not 100 sure

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