Geometry sem 1 7.1.2 Exam: Semester 1 Exam

How many line segments are needed to make a row of six triangles

Tanzania [10]

18 line segments also for faster and better u can 6 times 3 since there is already three in a triangle.

8 0

3 years ago

Which of the following is one solution to the expression (ax + b)(cx - d) = 0 ?

V125BC [204]

We know that
if (ax + b)(cx - d) = 0
then
(ax + b)= 0-----> ax=-b------> x=-b/a
and
(cx - d) = 0-----> cx=d------> x=d/c

therefore

the answer is the option
C. -\frac{b}{a}

4 0

3 years ago

Sums of a sequence: How many total gifts did my true love give to me during the entire 12 days of Christmas? Hint: Without any o

ale4655 [162]

On the first day of Christmas,
my true love sent to me
A partridge in a pear tree. On the second day of Christmas,
my true love sent to me
Two turtle doves,
And a partridge in a pear tree. On the third day of Christmas,
my true love sent to me
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

The song continues, adding 4 calling birds on the 4th day, 5 golden rings on the 5th, and so on up to the 12th day, when 12 drummers add to the cacophony of assorted birds, pipers and lords leaping all over the place.

Notice that on each day there is one partridge (so I will have 12 partridges by the 12th day), and each day from the second day onwards there are 2 doves (so I will have 22 doves), and from the 3rd there are 3 hens (total of 30 hens), and so on.

So, how many presents are there altogether?

Partridges: 1 × 12 = 12

Doves: 2 × 11 = 22

Hens 3 × 10 = 30

Calling birds: 4 × 9 = 36

Golden rings: 5 × 8 = 40

Geese: 6 × 7 = 42

Swans: 7 × 6 = 42

Maids: 8 × 5 = 40

Ladies: 9 × 4 = 36

Lords: 10 × 3 = 30

Pipers: 11 × 2 = 22

Drummers: 12 × 1 = 12

Total = 364

We observe that we have the same number of partridges as drummers (12 of each); doves and pipers (22 of each); hens and lords (30 of each) and so on. So the easiest way to count our presents is to add up to the middle of the list and then double the result: (12 + 22 + 30 + 36 + 40 + 42) × 2 = 364.

3 0

3 years ago

Read 2 more answers

The density of a block of wood with a volume of 50 cubic centimeters and mass off 100 grams is...................

Natalija [7]

Mass = 100 g

Volume = 50 cm³

Density :

D = m / V

D = 100 / 50

D = 2 g/cm³

answer A

hope this helps!.

4 0

3 years ago

Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f

GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in $\mathbb{R}$ .

$\\f(x)=(x^2+16)(x^2-2x-15)$

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

3 years ago

Geometry sem 1 7.1.2 Exam: Semester 1 Exam​

Geometry sem 1 7.1.2 Exam: Semester 1 Exam