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3 years ago

8

In the figure shown, suppose m angle ABC=n and m angle ABD=2(m angle DBC). The angle bisector of angle DBC is BE. What is m angl

e EBC

1 answer:

Yanka [14]3 years ago

4 0

Answer:

n/6

Step-by-step explanation:

If angle bisector of angle DBC is BE. What is m angle EBC, then <DBE = <EBC

Since <ABC = <ABD+<DBC

n = 2<DBC+<DBC

n = 3<DBC

<DBC = n/3

Since <DBC = 2EBC

n/3 = 2<EBC

n/6 = <EBC

Hence <EBC = n/6

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Approximately 40% of the calls to an airline reservation phone line result in a reservation being made. (round to three decimal

IRISSAK [1]

Answer:

The probability that none of the 10 calls result in a reservation is 0.60%. In turn, the probability that at least one call results in a reservation being made is 99.40%.

Step-by-step explanation:

Since approximately 40% of the calls to an airline reservation phone line result in a reservation being made, supposing an operator handles 10 calls, to determine what is the probability that none of the 10 calls result in a reservation, and what is the probability that at least one call results in a reservation being made, the following calculations must be performed:

0.6 ^ 10 = X

0.006 = X

0.006 x 100 = 0.60%

Therefore, the probability that none of the 10 calls result in a reservation is 0.60%.

100 - 0.60 = 99.40

In turn, the probability that at least one call results in a reservation being made is 99.40%.

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2 years ago

The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

$y=(x-5)^{2}+2$

Upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

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2 years ago

30 POINTS AND I WILL MARK BRAINLYEST

S_A_V [24]

Answer:

x intercept -7,0

y intercept 0,9

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3 years ago

baherus [9]

The correct answer is: [C]: " 5 " .
__________________________________________________________
→ " a = 5 " .
__________________________________________________________
Explanation:
__________________________________________________________

Given: " a + 1 <span>− 2 = 4 " ; Solve for "a" ;

4 + 2 = 6 ;

6 </span>− 1 = 5 ; → a = 5 ;

To check our work:

5 + 1 − 2 = ? 4 ?? ;

5 + 1 = 6 ;

6 − 2 = 4. Yes!

So the answer is: [C]: " 5 ".
_________________________________________________________
→ " a = 5 " .
_________________________________________________________

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3 years ago

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

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