MATHEMATICS HIGH SCHOOL

Which shows a perfect square trinomial?50y2 – 4x2
100 – 36x2y2
16x2 + 24xy + 9y2
49x2 – 70xy + 10y2

Answers

Answer 1
Answer:

Answer:

C. 16x^2+24xy+9y^2

Step-by-step explanation:

We have been given 4 expressions and we are asked to choose the expression that is a perfect square trinomial.

We know that a perfect square trinomial is in form: a^2+2ab+b^2.

Upon looking at our given choices we can see that option C is the correct choice as we can write as:

16x^2+24xy+9y^2=(4x)^2+2(4x\cdot 3y)+(3y)^2

16x^2+24xy+9y^2=(4x)^2+2(12xy)+(3y)^2

16x^2+24xy+9y^2=(4x)^2+24xy+(3y)^2

Therefore, option C is the correct choice.
Answer 2
Answer:

A perfect square trinomial is found in the expression where both the leading coefficients and the constant are both perfect squares. That only is the case with the third choice above. 16 is a perfect square of 4 times 4, and 9 is a perfect square of 3 times 3. We need to set it up into its perfect square factors and FOIL to make sure, so let's do that. Not only is 16 a perfect square in that first term, but so is x-squared. Not only is 9 a perfect square in the third term, but so is y-squared. So our factors will look like this:

(4x + 3y)(4x + 3y). FOIL that out to see that it does in fact give you back the polynomial that is the third choice down.

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The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the last step.9x2 +54x = 7

9(x2 + 6x) = 7

9(x2 + 6x + 9) = 7 +.?

Answers

Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left. 
9x2 +54x = 7

2. Make sure that the coefficient of the x^2 term is 1.
9(x2 + 6x) = 7

3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.
9(x2 + 6x + 9) = 7 + 81

9(x+3)^2 = 88

Answer:

? = 81

Step-by-step explanation:

How do I solve what is 2/3 of 90

Answers

The answer is 60.

Explanation:
In mathematics, the word "of" indicates multiply. This means we would multiply 2/3 * 90.

We can write 90 as a fraction by putting it over 1, which gives us 2/3(90/1).

To multiply fractions, we multiply straight across: (2*90)/(3*1) = 180/3 = 60.

Answer:

Thus, (2)/(3)* 90=60

Step-by-step explanation:

Given: (2)/(3) of 90

We have to write the simplified form of (2)/(3) of 90

Consider the given expression

(2)/(3) of 90

of means multiplication

thus, (2)/(3) of 90 means (2)/(3)* 90

Simplify, we have,

2* 30=60

Thus, (2)/(3)* 90=60

What Is The Value Of n So That The Expression X² + 12 x + n Is A Perfect Square Trinomial ?
A . 36
B . 36
C . 72
D . 144

Answers

The answer is 36 like (x+6)(x+6)

Terry bought some gum and some candy. The number of packs of chewing gum was one more than the number of mints. The number of mints was three times the number of chocolate bars. If gum cost 6 cents a pack, mints cost 3 cents each, and chocolate bars cost 10 cents each, how many of each confection did he get for 80 cents?

Answers

Mumber of mints=x
Number of packs of chewing gum=x+1
Number of chocolate bars=y

The number of mints was three times the number of chocolate bars; then
x=3y

We can suggest this system of equations:
x=3y
6(x+1)+3x+10y=80

we can solve this system of equations by substitution method.
6(3y+1)+3(3y)+10y=80
18y+6+9y+10y=80
18y+9y+10y=80-6
37y=74
y=74/37
y=2

x=3y
x=3*(2)=6

Number of mints=x=6
number of packs of chewing gum=x+1=6+1=7
number of chocolate bars=y=2

Answer: the number of mints is 6, the number of packs of chewing gum is 7, and the number of chocolate bars is 2.

Answer:

He bought 13 pkgs of gum

He bought 12 mints

He bought 4 candy bars

Step-by-step explanation:

Let +a+ = number of packages of gum Terry bought

Let +b+ = number of mints

Let +c+ = number of candy bars

------------------------------

(1) +a+=+b+%2B+1+

(2) +b+=+3c+

(3) +24a+%2B+10b+%2B+35c+=+572+ ( in cents )

-------------------------------------

There are 3 equations and 3 unknowns, so it's solvable

(2) +c+=+b%2F3+

Substitute (2) into (3)

(3) +24a+%2B+10b+%2B+35%2A%28+b%2F3%29+=+572+

Substitute (1) into (3)

(3) +24%2A%28+b+%2B+1+%29+%2B+10b+%2B+35%2A%28+b%2F3+%29+=+572+

(3) +24b+%2B+24+%2B+10b+%2B+%2835%2F3%29%2Ab+=+572+

Multiply both sides by +3+

(3) +3%2A34b+%2B+3%2A24+%2B+35b+=+3%2A572+

(3) +102b+%2B+72+%2B+35b+=+1716+

(3) +137b+=+1644+

(3) +b+=+12+

and

(1) +a+=+b+%2B+1+

(1) +a+=+12+%2B+1+

(1) +a+=+13+

and

(2) +c+=+b%2F3+

(2) +c+=+12%2F3+

(2) +c+=+4+

---------------------

He bought 13 pkgs of gum

He bought 12 mints

He bought 4 candy bars

-----------------------

check:

(3) +24a+%2B+10b+%2B+35c+=+572+ ( in cents )

(3) +24%2A13+%2B+10%2A12+%2B+35%2A4+=+572+

(3) +312+%2B+120+%2B+140+=+572+

(3) +572+=+572+

OK

What are the solution(s) to the quadratic equation 9x2 = 4?x =4/9 and x = -4/9
x = 2/3 and x = -2/3
x = 3/2 and x = -3/2
no real solution

Answers

we have

9x^(2)=4

Divide both sides by 9

9x^(2)/9=4/9

x^(2)=4/9

Square root both sides

x=(+/-)\sqrt{(4)/(9)}

x=(+/-)(2)/(3)

so

the solutions are

x1=(2)/(3)

x2=-(2)/(3)

therefore

the answer is the option

x = 2/3 and x = -2/3

The solutions to the quadratic equation; 9x2 = 4 are; x = 2/3 and x = -2/3.

Quadratic solutions

The given quadratic equation is;

  • 9x² = 4.

Hence, upon evaluation; we have;

  • x² = 4/9

Hence, x = ±2/3

Therefore, x = 2/3 and x = -2/3

Read more on quadratic solution;

brainly.com/question/1214333

Will mark brainlist for anyone who answers these parts correctly and properly showed their work.

Answers

Answer:

The rise is -5 the run is 4

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

=

-5

4

=

-1.25

θ =  

arctan(

ΔY

) + 360°

ΔX

=

308.65980825409°

ΔX = 2 – -2 = 4

ΔY = -1 – 4 = -5

Distance (d) = √ΔX2 + ΔY2 = √41 = 6.4031242374328

Equation of the line:

y = -1.25x + 1.5

or

y =  

-

5

x

4

+  

3

2

When x=0, y = 1.5

When y=0, x = 1.2

Please give brainliest PLZPLZ

I really hope this helps have a beautiful day
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