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3 years ago

which are perfect square trinomials? select two options A. x^2 -9 B. x^2 -100 C. x^2 - 4x + 4 D. x^2 +10x +25 E. x^2 +15x + 36

Mathematics

2 answers:

salantis [7]3 years ago

5 0

C and D
x^2 - 4x + 4 = (x-2)^2
x^2 + 10x +25 = (x+5)^2

Dmitry [639]3 years ago

4 0

Answer:

C. $x^2 - 4x + 4$

D. $x^2 +10x +25$

Step-by-step explanation:

A trinomial $ax^2+bx+c$ is perfect square trinomial if,

$D=b^2 - 4ac = 0$ ,

A. $x^2 -9$

By comparing,

a = 1, b = 0, c = -9,

$0^2 - 4\times 1\times -9\neq 0$

⇒ it is not a perfect square trinomial.

B. $x^2 -100$

By comparing,

a = 1, b = 0, c = -100,

$0^2 - 4\times 1\times -100\neq 0$

⇒ it is not a perfect square trinomial.

C. $x^2 - 4x + 4$

By comparing,

a = 1, b = -4, c = 4,

$(-4)^2 - 4\times 1\times 4=16-16=0$

⇒ it is a perfect square trinomial.

D. $x^2 +10x +25$

By comparing,

a = 1, b = 10, c = 25,

$10^2 - 4\times 1\times 25=100-100=0$

⇒ it is a perfect square trinomial.

E. $x^2 +15x + 36$

By comparing,

a = 1, b = 15, c = 36,

$15^2 - 4\times 1\times 36=225-144=81\neq 0$

⇒ it is not a perfect square trinomial.

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QveST [7]

Answer:

a) $x = -1$ and $y = 5$ , b) $x = 2$ and $y = -1$ , c) $x = -2$ and $y = 1$ , d) $x = 2$ and $y = -9$ , e) $x = 2$ and $y = -2$ , f) $x = 2$ and $y = -1$ , g) $x = 2$ and $y = -1$ , h) $x = 1$ and $y = 2$ .

Step-by-step explanation:

Each system is solved as follows (Cada sistema es resuelto como sigue):

a) $2\cdot x + y = 3$ and $3\cdot x - y = -8$

$y = 3 - 2\cdot x$

$3\cdot x - 3 + 2\cdot x = -8$

$5\cdot x = -5$

$x = -1$

$y = 5$

b) $x - 2\cdot y = 4$ and $-x+3\cdot y = -5$

$x = 4 + 2\cdot y$

$-4-2\cdot y+3\cdot y = - 5$

$-4+y = -5$

$y = -1$

$x = 2$

c) $-2\cdot x + 5\cdot y = 9$ and $x - y = -3$

$x = y-3$

$-2\cdot y +6 +5\cdot y = 9$

$3\cdot y = 3$

$y = 1$

$x = -2$

d) $5\cdot x - 4\cdot y = 2$ and $3\cdot x + 2\cdot y = -12$

$3\cdot x + 2\cdot y = -12$

$6\cdot x + 4\cdot y = -24$

$4\cdot y = -6\cdot x -24$

$5\cdot x +6\cdot x +24 = 2$

$11\cdot x = -22$

$x = 2$

$y = -9$

e) $x + y = 0$ and $2\cdot x +3\cdot y = -2$

$y = -x$

$2\cdot x -3\cdot x = -2$

$-x = -2$

$x = 2$

$y = -2$

f) $3\cdot x + 5\cdot y = 1$ and $x + y = 1$

$y = 1 - x$

$3\cdot x + 5 - 5\cdot x = 1$

$-2\cdot x = -4$

$x = 2$

$y = -1$

g) $5\cdot x - 2\cdot y = 12$ and $4\cdot x + 3\cdot y = 5$

$x = \frac{12+2\cdot y}{5}$

$x = \frac{5-3\cdot y}{4}$

$\frac{12+2\cdot y}{5} = \frac{5-3\cdot y}{4}$

$4\cdot (12+2\cdot y) = 5\cdot (5-3\cdot y)$

$48 + 8\cdot y = 25 - 15\cdot y$

$23\cdot y = -23$

$y = -1$

$x = 2$

h) $7\cdot x + 8\cdot y = 23$ and $3\cdot x + 2\cdot y = 7$

$3\cdot x + 2\cdot y = 7$

$12\cdot x + 8\cdot y = 28$

$8\cdot y = 28 - 12\cdot x$

$7\cdot x +28-12\cdot x = 23$

$-5\cdot x = -5$

$x = 1$

$y = 2$

8 0

3 years ago

who does the number, of zeros in the product of 8 and 5000 compara to the number of zeros in the factors ? explain.

mezya [45]

If one of the numbers we multiply (factors) has zeros at the end, and the other isn't a fraction: all those zeros will stay in the product.

But there might be additional zeros if the other numbers in the factors (the numbers which aren't 0) mupliply to "end" in zero and this is the case here:

8*5=40.

so the product will be 40 and the zeros of the 5000:

40 000

the number of zeros in the product will be bigger than the number of zeros in the factors if the non-zero parts of the fractions multiply to a number with 0 at the end.

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2 years ago

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avanturin [10]

Answer:

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Area: 1035.33 mm^2

Step-by-step explanation:

let x be the unknown sidelength

tan(41) = 30/x

x = 34.51

multiply by 30 to get area

7 0

3 years ago

Recycling one glass bottle can save enough energy to power an oven for 7.5 minutes. A glass bottle weighs 500 grams. Glass used

musickatia [10]

This is a units conversion problem: you have time and you want to convert that to money. Any units conversion problem involves multiplication by 1 in various forms. When you are given 7.5 min = 1 bottle = 500g, you know that (500 g)/(7.5 min) = 1 because the numerator and denominator are equal. (Of course, you are aware that 500 g = 0.500 kg.) The idea is to choose the forms of 1 that cause units you don't want to cancel, leaving only the units you do want.

$6\,h\times \dfrac{0.500\,kg}{7.5\,min}\times \dfrac{60\,min}{1\,h}\times \dfrac{5\,p}{1\,kg}\\\\=\dfrac{6\cdot 0.500\cdot 60\cdot 5\,p}{7.5\cdot 1\cdot 1}=120\,p$

The glass for recycling that would save enough energy to power an oven for 6 hours costs 120p.

3 0

2 years ago

Hey guys please help!!

Advocard [28]

Answer:

Yes

Step-by-step explanation:

g(x) = - $\frac{1}{4}$ x + $\frac{1}{4}$

y = - $\frac{1}{4}$ x + $\frac{1}{4}$ ....... (1)

(1) × 4

4y = - x + 1

x = - 4y + 1

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f(x) = - 4x + 1

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8 0

2 years ago

which are perfect square trinomials? select two options A. x^2 -9 B. x^2 -100 C. x^2 - 4x + 4 D. x^2 +10x +25 E. x^2 +15x + 36​

which are perfect square trinomials? select two options A. x^2 -9 B. x^2 -100 C. x^2 - 4x + 4 D. x^2 +10x +25 E. x^2 +15x + 36