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3 years ago

Which of the following is equivalent to 6x 2 + x - 12 ?

1 answer:

4 0

$6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\\\\=(2x-3)(3x+4)\\\\other\ method:\\\\6x^2+x-12\\a=6;\ b=1;\ c=-12\\\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{289}=17$

$x_1=\frac{-1-17}{2\cdot6}=\frac{-18}{12}=-\frac{3}{2};\ x_2=\frac{-1+17}{2\cdot6}=\frac{16}{12}=\frac{4}{3}\\\\6x^2+x-12=6(x+\frac{3}{2})(x-\frac{4}{3})=2\cdot3(x+\frac{3}{2})(x-\frac{4}{3})\\\\=2(x+\frac{3}{2})\cdot3(x-\frac{4}{3})=(2x+3)(3x-4)$

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Michael, Leo and JuWoong collect stamps. The ratio of the number of Michael's stamps to JuWoong's stamps is 2:7. The number of J

Alisiya [41]

Answer:

990

Step-by-step explanation:

M/J = 2/7

J = 3/4 L

L = M + 396

7M = 2J

J = 3.5M

3.5M = 3/4 L

L = 4/3(3.5M)

L = 14/3 M

14/3 M = M + 396

11/3 M = 396

M = 3/11 × 396

M = 108

L = M + 396

L = 108 + 396

L = 504

J = 3/4 L

J = 3/4 × 504

J = 378

M + L + J = 108 + 504 + 378 = 990

4 0

3 years ago

Sarah and her friends laid down two beach blankets. The blankets are the same length but of different widths. The distributive p

Masja [62]

Answer:The width of the orange blanket is 23 inches.

Step-by-step explanation:

The total of both lengths is 75.We know that the green blanket is 52 so 75-52 = 23 which is the width of the orange blanket

7 0

3 years ago

In a gambling game a person draws a single card from an ordinary 52-card playing deck. A person is paid $17 for drawing a jack o

Artyom0805 [142]

Answer:

$E.G=\$2$

Step-by-step explanation:

Sample size 52 card

Pay for J or Q $=\$17$

Pay for King or Ace $=\$5$

Pay for others $=-\$2$

Therefore

Probability of drawing J or Q

$P(J&Q)=\frac{8}{52}$

Probability or drawing King or Ace

$P(K or A)=\frac{8}{52}$

Probability or drawing Other cards

$P(O)=\frac{36}{52}$

Therefore

Expected Gain is mathematically given as

$E.G=\sum_xP(x)$

$E.G=17*\frac{8}{52}+5*\frac{8}{52}+(-2)*\frac{36}{52}$

$E.G=\$2$

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3 years ago

Find x in this 45°-45°-90° triangle.<br><br><br><br> x =

Zielflug [23.3K]

Use a^2 + b^2 = c^2

the triangle must be isosceles because the two angles are the same

1.2^2 + 1.2^2 = x^2
1.44 + 1.44 = x^2
2.88 = x^2
x=6√2/5
or
x ≈1.69706

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3 years ago

How can I rewrite this in exponential form and then evaluate it?

Vedmedyk [2.9K]

QUESTION:- EVALUATE THE EXPRESSION

EXPRESSION:-

${( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2}$

<h3>ANSWER-></h3>

${( \sqrt[6]{27 {a}^{3} {b}^{4} } )}^{2} \\ {( {27 {a}^{3} {b}^{4} } )}^{ \frac{2}{6} } \\ {({27 {a}^{3} {b}^{4} } )}^{ \frac{ \cancel{2}}{ \cancel6 {}^{ \: 3} } } \\ {(27)}^{ \frac{1}{3} } {a}^{ \frac{3}{3} } {b}^{ \frac{4}{3} } \\{(3)}^{ \frac{ \cancel3}{ \cancel3} } {a}^{ \frac{ \cancel3}{ \cancel3} } {b}^{\frac{3 + 1}{3} } \\3a {b}^{ \frac{ \cancel3}{ \cancel3} } {b}^{ \frac{1}{3} }$ $\\ ANSWER->3ab \sqrt[3]{b} \: \: \: \: \: or \: \: 3a {b}^{ \frac{4}{3} }$

6 0

3 years ago