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2 years ago

Given that ∠ABC ≅ ∠DBE, which statement must be true?

Mathematics

2 answers:

STALIN [3.7K]2 years ago

7 0

The second one which is ABD = CBE is the correct one

Airida [17]2 years ago

5 0

Answer:

ABD=CBE

Step-by-step explanation:

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Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x

spin [16.1K]

we have

$y-6x-9=0$

Step $1$

Clear the variable y

$y-6x-9=0$

Adds $(6x+9)$ both sides

$y-6x-9+(6x+9)=0+(6x+9)$

$y=(6x+9)$

Step $2$

Convert in function notation

Let

$f(x)=y$

$f(x)=(6x+9)$

therefore

the answer is

$f(x)=(6x+9)$

6 0

2 years ago

Read 2 more answers

Points H and F lie on circle c What is the length of line segment GH?

Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

$(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2}$ ......(ΔEGC is a right triangle)

$(GC)^{2} = (GE)^{2} +(EC)^{2}$

$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = x

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

$x (x-6) + 24 (x - 6) =0$

$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

3 0

1 year ago

Read 2 more answers

A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Co

harina [27]

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

8 0

1 year ago

Read 2 more answers

The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the contin

tatiyna

Answer:

a) The continuous rate of growth of this bacterium population is 45%

b) Initial population of culture at t = 0 is 950 bacteria

c) number of bacterial culture contain at t = 5 is 9013 bacteria

Step-by-step explanation:

The number of bacteria in a culture is given by

n(t) = 950 $e^{0.45t}$

a) rate of growth is

Bacteria growth model N(t) = no $e^{rt}$

Where r is the growth rate

hence r = 0.45

= 45%

b) Initial population of culture at t = 0

n(0) = 950 $e^{0.45(0)}$

= 950 $e^{0}$

= 950 bacteria

c) number of bacterial culture contain at t = 5

n(5) = 950 $e^{0.45(5)}$

= 950 $e^{2.25}$

= 9013.35

= 9013 bacteria

6 0

2 years ago

Find the square. (4x – 6y3)2

Artyom0805 [142]

Answer:

16x^2 -48xy^3 +36y^6

Step-by-step explanation:

Use FOIL or the distributive property or the form of the square of a binomial to expand the square.

(4x -6y^3)(4x -6y^3) = 4x(4x -6y^3) -6y^3(4x -6y^3)

= (4x)^2 -(4x)(6y^3) -(6y^3)(4x) +(6y^3)^2

= 16x^2 -48xy^3 +36y^6

_____

The form referred to above is ...

(a +b)^2 = a^2 +2ab +b^2

6 0

1 year ago