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3 years ago

Item 10

Mathematics

1 answer:

aev [14]3 years ago

6 0

Answer:

x/7<-3

x= >-28

Step-by-step explanation:

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the equation -2x^2+3=-9x is rewritten in the form of -2(x-p)^2 +q=0. What is the value of q?the equation -2x^2+3=-9x is rewritte

Novosadov [1.4K]

Value of q is $\frac{105}{8}$ .

<u>Step-by-step explanation:</u>

We have , the equation $-2x^2+3=-9x$ is rewritten in the form of $-2(x-p)^2 +q=0$ . We need to find What is the value of q . Let's find out:

Let's simplify equation $-2x^2+3=-9x$ into $-2(x-p)^2 +q=0$ :

⇒ $-2x^2+3=-9x$

⇒ $-2x^2+9x+3=0$

⇒ $2x^2-9x=3$

⇒ $2(x^2-\frac{9}{2}x)=3$

⇒ $(x^2-\frac{9}{2}x)=\frac{3}{2}$

⇒ $(x^2-2(1)\frac{9}{4}x)=\frac{3}{2}$

⇒ $(x^2-2(1)\frac{9}{4}x) + (\frac{9}{4})^2=\frac{3}{2} + (\frac{9}{4})^2$

⇒ $(x-\frac{9}{4})^2=\frac{3}{2} + (\frac{81}{16})$

⇒ $(x-\frac{9}{4})^2=\frac{24}{16} + (\frac{81}{16})$

⇒ $(x-\frac{9}{4})^2=\frac{105}{16}$

⇒ $-2(x-\frac{9}{4})^2=-2(\frac{105}{16})$

⇒ $-2(x-\frac{9}{4})^2=-\frac{105}{8}$

⇒ $-2(x-\frac{9}{4})^2+\frac{105}{8} = 0$

Comparing this equation to $-2(x-p)^2 +q=0$ , $q =\frac{105}{8}$ .

Therefore ,Value of q is $\frac{105}{8}$ .

8 0

3 years ago

how do you indicate congruent segments in a diagram? how do you indicate congruent angles in a diagram?

ICE Princess25 [194]

9514 1404 393

Answer:

segments: using the same number of hash marks
angles: using the same number of arcs, or hash marks on an arc

Step-by-step explanation:

The attached diagram shows that segments AC and BD are congruent by using a single hash mark on each of those segments. If other segments are congruent, but not congruent to these two, the "decoration" would be different, probably two hash marks. Segments marked with the same "decoration" are intended to be understood as congruent.

The "decoration" used for congruent angles is an arc of some kind. Here, a single arc is used to signify angle CAB is congruent to angle DBA. Additional arcs could be used for other congruent angles, or hash marks can be put on the arcs.