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3 years ago

Help asap! Thanks in advance! There's two questions btw:)

Mathematics

1 answer:

lutik1710 [3]3 years ago

6 0

Answer:

[1].

Option A and D are correct.

[2].

Option A is correct

Step-by-step explanation:

[1].

Quadratic function states that it is an equation of second degree i.,e it contains at least one term that is squared.

The standard form of the quadratic equation is; $ax^2+bx+c = 0$

$y(y+4)-y = 6$

Using distributive property: $a\cdot (b+c) = a\cdot b + a\cdot c$

$y^2+4y-y=6$

Combine like terms;

$y^2+3y = 6$

$y^2+3y -6=0$ which represents a quadratic equation.

$3a-7 = 2(7a-3)$

$3a-7 = 14a-6$

$11a+1 = 0$ which is not a quadratic equation.

(3x+2)+(6x-1) = 0

Combine like terms;

9x +1 = 0 which is not a quadratic equation.

4b(b) = 0

$4b^2 = 0$ which represents the quadratic equation.

[2].

Given the parent function: $y=x^2$

The reflection rule over x axis is given by;

$(x, y) \rightarrow (x, -y)$

then

the function become: $y = -x^2$

Vertical shift:

If c is a positive real number, the graph y=f(x)+c is the graph of y =f(x) shifted upward c units.

If c is a positive real number, the graph y=f(x)-c is the graph of y =f(x) shifted downward c units.

then;

The graph $y=-x^2-3$ is the graph of $y=-x^2$ shifted 3 units down.

Therefore, the translation of the graph of $y=x^2$ to obtain $y=-x^2-3$ is, reflect over the x-axis and shift down 3

You might be interested in

Evaluate the following 9+(-3)

Karo-lina-s [1.5K]

9+-3 means 9 plus 3 less
basically it is 9-3=6

5 0

2 years ago

Read 2 more answers

DNA molecules consist of chemically linked sequences of the bases adenine, guanine, cytosine and thymine, denoted A, G, C and T.

Dmitry [639]

Answer:

1. See the attached tree diagram (64 different sequences); 2. 64 codons; 3. 8 codons; 4. 24 codons consist of three different bases.

Step-by-step explanation:

The main thing to solve this kind of problem, it is to know if the pool of elements admits <em>repetition</em> and if the <em>order matters</em> in the sequences or collections of objects that we can form.

In this problem, we have the bases of the DNA molecule, namely, adenine (A), thymine (T), guanine (G) and cytosine (C) and they may appear in a sequence of three bases (codon) more than once. In other words, <em>repetition is allowed</em>.

We can also notice that <em>order matters</em> in this problem since the position of the base in the sequence makes a difference in it, i.e. a codon (ATA) is different from codon (TAA) or (AAT).

Then, we are in front of sequences that admit repetitions and the order they may appear makes a difference on them, and the formula for this is as follows:

$\\ Sequences\;with\;repetition = n^{k}$ (1)

They are sequences of <em>k</em> objects from a pool of <em>n</em> objects where the order they may appear matters and can appeared more than once (repetition allowed).

<h3>1 and 2. Possible base sequences using tree diagram and number of possible codons</h3>

Having all the previous information, we can solve this question as follows:

All possible base sequences are represented in the first graph below (left graph) and are 64 since <em>n</em> = 4 and <em>k</em> = 3.

$\\ Sequences\;with\;repetition = 4^{3} = 4*4*4 = 64$

Looking at the graph there are 4 bases * 4 bases * 4 bases and they form 64 possible sequences of three bases or codons. So <em>there are 64 different codons</em>. Graphically, AAA is the first case, then AAT, the second case, and so on until complete all possible sequences. The second graph shows another method using a kind of matrices with the same results.

<h3>3. Cases for codons whose first and third bases are purines and whose second base is a pyrimidine</h3>

In this case, we also have sequences with <em>repetitions</em> and the <em>order matters</em>.

So we can use the same formula (1) as before, taking into account that we need to form sequences of one object for each place (we admit only a Purine) from a pool of two objects (we have two Purines: A and G) for the <em>first place</em> of the codon. The <em>third place</em> of the codon follows the same rules to be formed.

For the <em>second place</em> of the codon, we have a similar case: we have two Pyrimidines (C and T) and we need to form sequences of one object for this second place in the codon.

Thus, mathematically:

$\\ Sequences\;purine\;pyrimidine\;purine = n^{k}*n^{k}*n^{k} = 2^{1}*2^{1}*2^{1} = 8$

All these sequences can be seen in the first graph (left graph) representing dots. They are:

$\\ \{ATA, ATG, ACA, ACG, GTA, GTG, GCA, GCG\}$

The second graph also shows these sequences (right graph).

<h3>4. Possible codons that consist of three different bases</h3>

In this case, we have different conditions: still, order matters but no repetition is allowed since the codons must consist of three different bases.

This is a case of <em>permutation</em>, and the formula for this is as follows:

$\\ nP_{k} = \frac{n!}{n-k}!$ (2)

Where n! is the symbol for factorial of number <em>n</em>.

In words, we need to form different sequences (order matters with no repetition) of three objects (a codon) (k = 3) from a pool of four objects (n = 4) (four bases: A, T, G, and C).

Then, the possible number of codons that consist of three different bases--using formula (2)--is:

$\\ 4P_{3} = \frac{4!}{4-3}! = \frac{4!}{1!} = \frac{4!}{1} = 4! = 4*3*2*1 = 24$

Thus, there are <em>24 possible cases for codons that consist of three different bases</em> and are graphically displayed in both graphs (as an asterisk symbol for left graph and closed in circles in right graph).

These sequences are:

{ATG, ATC, AGT, AGC, ACT, ACG, TAG, TAC, TGA, TGC, TCA, TCG, GAT, GAC, GTA, GTC, GCA, GCT, CAT, CAG, CTA, CTG, CGA, CGT}

<h3 />

6 0

3 years ago

10 POINTS PLEASE HELP

Llana [10]

Answer:

A company sells tents in two styles, shown below.

The sides and floor of each tent made of nylon.

For tunnel tent:

In a composite figure of tunnel tent :

There are two semi circle, half cylindrical shape and its base is made of Square.

Area of semi-circle is given by:

where r is the radius the circle.

Here, Diameter(d) = 8 feet

We know that: Diameter(d) = 2 r

then;

8 = 2r

⇒ r= 4 ft.

Area of square =

then;

Area of square = square ft

Lateral surface area of cylinder = where r is the radius and h is the height

Here, h = 8 ft

Lateral surface area of half cylinder = square ft

Total Surface area of tunnel tent(S)=2(Area of semi-circle)+(Lateral surface area of half cylindrical)+(Area of square)

Substitute the given values we have;

square ft.

For Pup tent:

Each side of tent = 8 ft

In a figure of Pup tent:

There are 3 square shape and two triangle.

Area of square =

then;

Area of square = square ft

Area of a triangle is given by:

Each side of a triangle is same.

This is an equilateral triangle, and its height is given by:

then;

Area of triangle = square ft.

Substitute the given values we have;

Total surface area of Pup tent(S')

= square ft.

⇒S' > S

therefore, the tunnel tent require less nylon to manufacture.

<h2 /><h2>PLZ GIMME BRAINLIEST :)) !!!!!!</h2>

6 0

3 years ago

Please help.................

evablogger [386]

It usually works well to do what the instructions tell you. Multiply each diameter by 3.14.

a) 3.14×6 cm = 18.84 cm

b) [can't read the picture]

d) 3.14×9 in = 28.26 in

e) 3.14×11 mm = 34.54 mm

7 0

3 years ago

How do I solve this equation

Anestetic [448]

-x - y = 8
2x - y = -1

Ok, we are going to solve this in 2 parts. First we have to solve for one of the variables in one of the equation in terms of the other variable. I like to take the easiest equation first and try to avoid fractions, so let's use the first equation and solve for x.

-x - y = 8 add y to each side
-x = 8 + y divide by -1
x = -8 - y

So now we have a value for x in terms of y that we can use to substitute into the other equation. In the other equation we are going to put -8 - y in place of the x.

2x - y = -1
2(-8 - y) - y = -1 multiply the 2 through the parentheses
-16 - 2y - y = -1 combine like terms
-16 - 3y = -1 add 16 to both sides
-3y = 15 divide each side by -3
y = -5

Now we have a value for y. We need to plug it into either of the original equations then solve for x. I usually choose the most simple equation.

-x - y = 8
-x - (-5) = 8 multiply -1 through the parentheses
-x + 5 = 8 subtract 5 from each side
-x = 3 divide each side by -1
x = -3

So our solution set is

(-3, -5)

That is the point on the grid where the 2 equations are equal, so that is the place where they intersect.

4 0

3 years ago