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3 years ago

4xsquared - 9=0? could anyone help me solve this quadratic equation by FACTORING?

1 answer:

7 0

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\
4x^2-9=0\implies 2^2x^2-3^2=0\implies (2x)^2-3^2=0
\\\\\\\
[(2x)-3][(2x)+3]=0\implies 
\begin{cases}
2x-3=0\\
2x=3\\
x=\frac{3}{2}\\
------\\
2x+3=0\\
2x=-3\\
x=-\frac{3}{2}
\end{cases}$

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100 points! Mhanifa can you please help? Look at the picture attached. I will mark brainliest!

dimulka [17.4K]

Answer:

1 and 2.

Midpoints calculated, plotted and connected to make the triangle DEF, see the attached.

D= (-2, 2), E = (-1, -2), F = (-4, -1)

As per definition, midsegment is parallel to a side.

Parallel lines have same slope.

Find slopes of FD and CB and compare.

m(FD) = (2 - (-1))/(-2 -(-4)) = 3/2
m(CB) = (1 - (-5))/(1 - (-3)) = 6/4 = 3/2
As we see the slopes are same

Find the slopes of FE and AB and compare.

m(FE) = (-2 - (- 1))/(-1 - (-4)) = -1/3
m(AB) = (1 - 3)/(1 - (-5)) = -2/6 = -1/3
Slopes are same

Find the slopes of DE and AC and compare.

m(DE) = (-2 - 2)/(-1 - (-2)) = -4/1 = -4
m(AC) = (-5 - 3)/(-3 - (-5)) = -8/2 = -4
Slopes are same

As per definition, midsegment is half the parallel side.

We'll show that FD = 1/2CB

FD = $\sqrt{(2+1)^2+(-2+4)^2}$ = $\sqrt{3^2+2^2}$ = $\sqrt{13}$
CB = $\sqrt{(1 + 5)^2+(1+3)^2}$ = $\sqrt{6^2+4^2}$ = 2 $\sqrt{13}$
As we see FD = 1/2CB

FE = 1/2AB

FE = $\sqrt{(-4+1)^2+(-1+2)^2}$ = $\sqrt{3^2+1^2}$ = $\sqrt{10}$
AB = $\sqrt{(-5 -1)^2+(3-1)^2}$ = $\sqrt{6^2+2^2}$ = 2 $\sqrt{10}$
As we see FE = 1/2AB

DE = 1/2AC

DE = $\sqrt{(-2+1)^2+(2+2)^2}$ = $\sqrt{1^2+4^2}$ = $\sqrt{17}$
AC = $\sqrt{(-5 +3)^2+(3+5)^2}$ = $\sqrt{2^2+8^2}$ = 2 $\sqrt{17}$
As we see DE = 1/2AC

3 0

3 years ago

Read 2 more answers

Can someone PLEASE answer this and explain I really need help I’ll mark brainliest

svetlana [45]

Answer:

Michael = x÷7

lee = 2(x÷7)

(x÷7)+2(x÷7)

Step-by-step explanation:

since he earns x dollars every seven days, to get the amount he earns, you divide that amount by 7 and for Lee, she gets twice as much so you multiply Michael's amount by 2

7 0

2 years ago

I need help finding the measures of the other angles.

Alex Ar [27]

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3 years ago

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how is building a triangle with different side lengths given different than building a quadrilateral with given side lengths?

Mariana [72]

Answer:

there can only be one possibility for a triangle when given the lengths of all the sides but for a quadrilateral the measure of the angles could differ depending on the person building the,. this is because triangles are more stable than quadrilaterals meaning that their side lengths follow a lot more rules than quadrilaterals do, for example the length of the side lengths can indicate whether or not that triangle is an acute, obtuse, or right triangle, and this is also evident by considering that you can use the SSS theorem to indicate two triangles are congruent, but for quadrilaterals you cant do that

Step-by-step explanation:

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3 years ago

5. (07.09) Given the functions f(x) = 7x+13 and g(x)=x+2. which of the following functions represents f(g(x)] correctly? (2 poin

lapo4ka [179]

Answer:

f(g(x)) = 7x + 27

Step-by-step explanation:

We have, f(x) = 7x+13 and g(x) = x+2.

So, the function f(g(x)) is obtained by substituting the function g(x) = x+2 in f(x) = 7x+13,

i.e. f(g(x)) = f(x+2)

i.e. f(g(x)) = 7 × (x+2) + 13

i.e. f(g(x)) = 7x + 14 + 13

i.e. f(g(x)) = 7x + 27

Thus, f(g(x)) = 7x + 27

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2 years ago