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3 years ago

Graph the image of the given triangle, translated 4 units to the right and 5 units down.

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

8 0

Here the photo is attached

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The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find<br> b.

inna [77]

Given that the difference between the roots of the equation $3x^2+bx+10=0$ is $4 \frac{1}{3} = \frac{13}{3}$ .

Recall that the sum of roots of a quadratic equation is given by $- \frac{b}{a}$ .

Let the two roots of the equation be $\alpha$ and $\alpha + \frac{13}{3}$ , then

$\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3} \\ \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3}$ . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by $\frac{c}{a}$ , thus:

$\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3} \\ \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3}$ . . . (2)

From (1), we have:

$2 \alpha =- \frac{b}{3} - \frac{13}{3} \\ \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}$

Substituting for alpha into (2), gives:

$\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\ \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36} \\ \\ \Rightarrow b^2=289 \\ \\ \Rightarrow b=\pm\sqrt{289}=\pm17$

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3 years ago

The number on top of a fraction is called the

olga2289 [7]

The number on top of a fraction is the numerator. The number on the bottom of the fraction is the denominator.

Example : 2/3....the 2 is the numerator and the 3 is the denominator

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Do you guys know how to multiply decimals because I can’t I forgot! What’s 87.8 Times 66.4

Mrac [35]

5829.92

you multiply it as you would regular numbers and then you count the places that the decimal is in front of. in this case it would be 2 numbers, then in the number you got by multiplying, move the decimal 2 places up

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insens350 [35]

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Step-by-step explanation:

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Please Answer This, the question is on the picture. it needs to be a fraction

tino4ka555 [31]

Answer:

x = 33

Step-by-step explanation:

sin 29° = 16/x

x = 33

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