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3 years ago

Write the inequality: The sum of x and 10 is less than -4

Mathematics

1 answer:

andrezito [222]3 years ago

4 0

Answer:

x + 10 < -4

Step-by-step explanation:

x + 10 is less than -4, so -4 would have to be greater. You would put x + 10 on the left side and on the right side would be -4. In between would be a less than sign because x + 10 is LESS than -4.

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Does anyone know the answers to this test???OFFERING LOTS PF POINTS. Just Incase the picture isn’t loading it’s the parametric f

steposvetlana [31]

Answer:

The correct choice is C

Step-by-step explanation:

The given curve is described by the parametric equations:

$x=4-t$

$y=t^2-2$

Let us eliminate the parameter by making t the subject in the first equation and substitute into the second equation;

$t=4-x$

We substitute this into the second equation to get:

$y=(4-x)^2-2$

This is the equation of a parabola whose vertex is at (4,-2)

The correct choice is C

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3 years ago

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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Answer:

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