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2 years ago

Armando and Bianca are 290 feet apart when they start walking toward one another. Bianca walks twice as fast as

Mathematics

1 answer:

aivan3 [116]2 years ago

3 0

9514 1404 393

Answer:

d = 290 -3x

Step-by-step explanation:

For each x feet that Armondo travels toward Bianca, Bianca travels 2x feet toward Armondo. The net effect is that the distance between them decreases by x+2x = 3x feet. The distance starts at 290 feet when x=0, so the distance can be described by ...

d = 290 -3x

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In the circle below, DB = 22 cm, and m<DBC = 60°. Find BC. Ignore my handwriting.

Karo-lina-s [1.5K]

Answer:

$BC=11\ cm$

Step-by-step explanation:

step 1

Find the measure of the arc DC

we know that

The inscribed angle measures half of the arc comprising

$m\angle DBC=\frac{1}{2}[arc\ DC]$

substitute the values

$60\°=\frac{1}{2}[arc\ DC]$

$120\°=arc\ DC$

$arc\ DC=120\°$

step 2

Find the measure of arc BC

we know that

$arc\ DC+arc\ BC=180\°$ ----> because the diameter BD divide the circle into two equal parts

$120\°+arc\ BC=180\°$

$arc\ BC=180\°-120\°=60\°$

step 3

Find the measure of angle BDC

we know that

The inscribed angle measures half of the arc comprising

$m\angle BDC=\frac{1}{2}[arc\ BC]$

substitute the values

$m\angle BDC=\frac{1}{2}[60\°]$

$m\angle BDC=30\°$

therefore

The triangle DBC is a right triangle ---> 60°-30°-90°

step 4

Find the measure of BC

we know that

In the right triangle DBC

$sin(\angle BDC)=BC/BD$

$BC=(BD)sin(\angle BDC)$

substitute the values

$BC=(22)sin(30\°)=11\ cm$

6 0

3 years ago

f(x) = 4x^2+2x+6f(x)=4x 2 +2x+6f, left parenthesis, x, right parenthesis, equals, 4, x, squared, plus, 2, x, plus, 6 What is the

vladimir2022 [97]

Given:

The given function is $f(x)=4x^2+2x+6$

We need to determine the value of the discriminant f and also to determine the distinct real number zeros of f.

Discriminant:

The discriminant can be determined using the formula,

$\Delta = b^2-4ac$

Now, we shall determine the discriminant of the function $f(x)=4x^2+2x+6$

Substituting the values in the formula, we have;

$\Delta=(2)^2-4(4)(6)$

$\Delta=4-96$

$\Delta=-92$

Thus, the value of the discriminant of f is -92.

Distinct roots:

The distinct zeros of the function f can be determined by

(1) If $\Delta>0$ , then the function has 2 real roots.

(2) If $\Delta=0$ , then the function has 2 real roots ( or one repeated root).

(3) If $\Delta$ , then the function has 2 imaginary roots (or no real roots).

Since, the discriminant is $\Delta=-92 \ < \ 0$ , then the function has no real roots or 2 imaginary roots.

Thus, the function has 2 imaginary roots.

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3 years ago

What is the simplified form of the square root of 80?

djyliett [7]

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Try this:
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2 years ago