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torisob [31]
3 years ago
6

I need help ASAP pleaseee

Mathematics
1 answer:
Tanya [424]3 years ago
3 0

Answer:Price of laptop A = $1220

Step-by-step explanation:

Sum of the price: A + B = 2185

Sum of the price: A + C = 2571

B : C = 5 : 7

B = 5/7 × C

So, replace the B:

A + 5/7 C = 2185

A + C = 2571

Eliminate by subtracting the first from the second: 2/7 C = 386

C = 1351

So, A = 2571 - 1351 = 1220

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Can you please help me give the Complete solution <br><br>(nonsence report )​
Tasya [4]

\huge \boxed{\mathfrak{Question} \downarrow}

  • Factorise the polynomials.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

__________________

<h3><u>1. x² + 4x + 4</u></h3>

{x}^{2}  + 4x + 4

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+4. To find a and b, set up a system to be solved.

a+b=4  \\ ab=1\times 4=4

As ab is positive, a and b have the same sign. As a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

1,4  \\ 2,2

Calculate the sum for each pair.

1+4=5  \\ 2+2=4

The solution is the pair that gives sum 4.

a=2 \\  b=2

Rewrite x² + 4x + 4 as (x² + 2x) + (2x + 4)

\left(x^{2}+2x\right)+\left(2x+4\right)

Take out the common factors.

x\left(x+2\right)+2\left(x+2\right)

Factor out common term x+2 by using distributive property.

\left(x+2\right)\left(x+2\right)

Rewrite as a binomial square.

b. \:  \:  \boxed{ \boxed{{(x + 2)}^{2} }}

__________________

<h3><u>2. x² - 8x + 16</u></h3>

x ^ { 2 } - 8 x + 16

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+16. To find a and b, set up a system to be solved.

a+b=-8  \\ ab=1\times 16=16

As ab is positive, a and b have the same sign. As a+b is negative, a and b are both negative. List all such integer pairs that give product 16.

-1,-16  \\ -2,-8  \\ -4,-4

Calculate the sum for each pair.

-1-16=-17  \\ -2-8=-10  \\ -4-4=-8

The solution is the pair that gives sum -8.

a=-4  \\ b=-4

Rewrite x²-8x+16 as \left(x^{2}-4x\right)+\left(-4x+16\right).

\left(x^{2}-4x\right)+\left(-4x+16\right)

Take out the common factors.

x\left(x-4\right)-4\left(x-4\right)

Factor out common term x-4 by using distributive property.

\left(x-4\right)\left(x-4\right)

Rewrite as a binomial square.

d. \:  \:  \boxed{\boxed{\left(x-4\right)^{2} }}

__________________

<h3><u>3. 4x² + 12xy + 9y²</u></h3>

4 x ^ { 2 } + 12 x y + 9 y ^ { 2 }

Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=2x and b=3y.

e. \:  \: \boxed{ \boxed{\left(2x+3y\right)^{2} }}

__________________

<h3><u>4. x⁴ - 2x² + 1</u></h3>

x ^ { 4 } - 2 x ^ { 2 } + 1

To factor the expression, solve the equation where it equals to 0.

x^{4}-2x^{2}+1=0

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 1 and q divides the leading coefficient 1. List all candidates p/q.

± \: 1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=1

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x⁴-2x²+1 by x-1 to get x³+x²-x-1. To factor the result, solve the equation where it equals to 0.

x^{3}+x^{2}-x-1=0

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -1 and q divides the leading coefficient 1. List all candidates p/q.

± \:  \: 1

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

x=1

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x³+x²-x-1 by x-1 to get x²+2x+1. To factor the result, solve the equation where it equals to 0.

x^{2}+2x+1=0

All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 2 for b and 1 for c in the quadratic formula.

x=\frac{-2±\sqrt{2^{2}-4\times 1\times 1}}{2}  \\

Do the calculations.

x=\frac{-2±0}{2}  \\

Solutions are the same.

x=-1

Rewrite the factored expression using the obtained roots.

\left(x-1\right)^{2}\left(x+1\right)^{2}  \\  = a. \:  \:  \boxed{ \boxed{\left(x^{2}-1\right)^{2}}}

__________________

  • <em>Refer to the attached picture too.</em>

7 0
3 years ago
Suppose a triangle with angles measuring 37°, 59°, and 84° is reflected across the y-axis of a coordinate grid. Which would be t
stich3 [128]
I'm assuming there are supposed to be choices, but if a figure goes through only a reflection, then the angle measures will not change.
4 0
4 years ago
What are the slope and y-intercept of the linear function graphed to the left? slope: –2; y-intercept: 2 slope: ; y-intercept: 1
Anon25 [30]

Let

A(0,1)\\  B(2,0)

we know that

The y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point A is the y-intercept

y=1

<u>The answer part a) is</u>

The value of y-intercept is 1

<u>Part b)</u> Find the slope m

we know that

the value of the slope is equal to

m =\frac{(y2-y1)}{(x2-x1)}

Substitute the values

m =\frac{(0-1)}{(2-0)}

m =-\frac{1}{2}

therefore

<u>the answer Part b) is</u>

The value of the slope is equal to -\frac{1}{2}

<u>The general answer is</u>

The slope is -\frac{1}{2}

The value of y-intercept is 1

4 0
3 years ago
Read 3 more answers
Someone please Help me ASAP! You would be a blessing!
ozzi

11. Let the Number of Students filled in One Van be : V

Let the Number of Students filled in One Bus be : B

Given : The Senior Class of High School A rented and filled 8 Vans and 3 Buses with 150 students

⇒ 8V + 3B = 150 --------------- [1]

Given : The Senior Class of High School B rented and filled 10 Vans and 3 Buses with 162 students

⇒ 10V + 3B = 162 --------------- [2]

Subtracting Equation [1] from Equation [2], we get :

⇒ (10V + 3B) - (8V + 3B) = 162 - 150

⇒ 10V - 8V + 3B - 3B = 12

⇒ 2V = 12

⇒ V = 6

Substituting V = 6 in Equation [1], We get :

⇒ 8(6) + 3B = 150

⇒ 48 + 3B = 150

⇒ 3B = 150 - 48

⇒ 3B = 102

⇒ B = 34

⇒ Each Van can carry 6 Students

⇒ Each Bus can carry 34 students

12 . Let the Price of One Adult Ticket be : A

Let the Price of One Student Ticket be : S

Given : On the First Day, The School sold 6 Adult tickets and  7 student tickets for a Total of $122

⇒ 6A + 7S = 122 ----------- [1]

Given : On the Second Day, The School sold 6 Adult tickets and  6 student tickets for a Total of $114

⇒ 6A + 6S = 114 ----------- [2]

Subtracting Equation [2} from Equation [1], We get :

⇒ (6A + 7S) - (6A + 6S) = 122 - 114

⇒ 6A - 6A + 7S - 6S = 8

⇒ S = 8

Substituting S = 8 in Equation [1], We get :

⇒ 6A + 7(8) = 122

⇒ 6A + 56 = 122

⇒ 6A = 122 - 56

⇒ 6A = 66

⇒ A = 11

⇒ Price of One Adult Ticket = $11

⇒ Price of One Student Ticket = $8

3 0
4 years ago
n their last basketball game, Becky scored twice as many points as Min. Together, they scored 42 points. How many points did Bec
Makovka662 [10]

Becky =B

Min =M

B =2M and B + M = 42.

(2M) + M= 3M = 42 and so M=42/3=14.

B = 2M so it's 14*2=28


Becky scored 28 points.

4 0
3 years ago
Read 2 more answers
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