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7 months ago

Simplify expression(5x^2-2x+3)+(-6x^2+4x-7)

Mathematics

1 answer:

Natali5045456 [20]7 months ago

3 0

Given the expression:

$\mleft(5x^2-2x+3\mright)+\mleft(-6x^2+4x-7\mright)$

To simplify the expression, we will combine the like terms

so,

$\begin{gathered} \mleft(5x^2-2x+3\mright)+\mleft(-6x^2+4x-7\mright) \\ =(5x^2-6x^2)+(-2x+4x)+(3-7) \\ \\ =-x^2+2x-4 \end{gathered}$

So, the answer will be:

$-x^2+2x-4$

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Use the work shown to find the solutions of the quadratic equation. x2 – x –3/4=0 x2 – x = 3/4

bija089 [108]

Answer:

x = - $\frac{1}{2}$ , x = $\frac{3}{2}$

Step-by-step explanation:

Given

x² - x - $\frac{3}{4}$ = 0

Multiply through by 4 to clear the fraction

4x² - 4x - 3 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 3 = - 12 and sum = - 4

The factors are + 2 and - 6

Use these factors to split the x- term

4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term

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

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - $\frac{1}{2}$

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

8 0

2 years ago

12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5

Murljashka [212]

Answer:

$\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}$

Step-by-step explanation:

$\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/$

$\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}$

$\text{Despite this, let's check the ratios}$

$\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5$

$\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}$