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3 years ago

ASAP PLEASE IM BEHINF AND NEED TO SUMBIT ALL WORK BY 12!!!!!!!!!

Mathematics

2 answers:

saul85 [17]3 years ago

7 0

Answer: The second graph

Step-by-step explanation: X must be greater than 11 and the filled in circle means it could also be 11.

Yuri [45]3 years ago

6 0

Answer:

see below

Step-by-step explanation:

x ≥11

Since there is an equals sign we have a closed circle at 11

X is greater so the line goes to the left

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What does it mean by Solve the exponential equation for x?

raketka [301]

It varies from problem to problem, but the two common ways to solve exponential equations are either by "equating the bases" or using logarithms to break them down. For example, if you have something like 5ˣ - 1 = 6, you only have one exponent involved, so there aren't any bases to equate.

5ˣ - 1 = 6 ... add 1 to both sides

5ˣ = 7 ... you have one term on either side, so take the log of both sides

log 5ˣ = log 7 ... by exponent properties, you can now bring that x out front

x log 5 = log 7 ...solve for x, divide both sides by log 5

x = (log 7)/(log 5)

That's a really simple example, but it applies the same to problems like 5ˣ⁺³ - 1 = 6, too. Same exact process. Get the exponent alone, take the log of both sides, solve for x.

For equating the bases, if you have something like

2ˣ = 4ˣ⁺²

you can recognize that 4 and 2 are multiples of one another. In fact, 4 = 2². So in this case, you play around with squares to get something where the bases of the exponents (i.e. the number being squared, or cubed, or set to the xth power) match.

2ˣ = 4ˣ⁺² ... but 4 = 2^2, so write it in this form instead

2ˣ = (2²)ˣ⁺² ... by exponent rules, you multiply the exponents on the righthand side, so distribute 2 to x + 2

2ˣ = 2²ˣ⁺⁴

And problems like this are really nice, if you can equate the bases using square roots and cube roots, because what you can do now is totally get rid of the 2's on either side and just drop it down to x = 2x + 4, then solve for x. The math behind this is:

2ˣ = 2²ˣ⁺⁴ ... single exponent on either side, so you can take the log of both sides

log 2ˣ = log 2²ˣ⁺⁴ ... bring the exponents out front

x log 2 = (2x + 4) log 2 ... divide both sides by log 2

x = 2x + 4

So once you know that property, you can skip a little work. Solving an exponential equation for x almost always involves a logarithm, and you should look into properties of exponents. They'll help you manipulate the problem by writing stuff in different forms so you can find the answer.

8 0

3 years ago

Quadrilateral ABCD is a parallelogram. Given this, fill in the coordinates below.

Lubov Fominskaja [6]

Answer:

The coordinates of D are (8,3)

Step-by-step explanation:

We have quadrilateral ABCD being a parallelogram with coordinates A(3,2), B(5,4), C(10,5), and D(a,b).

We want to find the coordinates of D.

Since ABCD is a parallelogram, the diagonals AC and BD bisects each other.

The midpoint of AC is (13/2,7/2).

This is also the midpoint of BD.

By the midpoint rule:

$( \frac{5 + a}{2} , \frac{4 + b}{2} ) = ( \frac{13}{2} , \frac{7}{2} )$

This implies that:

$5 + a = 13 \\ a = 13 - 5 \\ a = 8$

Similarly,

$4 + b = 7 \\ b = 7 - 4 \\ b = 3$

The coordinates of D are (8,3)

8 0

3 years ago

Select the correct answer from the drop-down menu. a coin is biased to display heads 75% of the time. it is tossed 20 times, and

ella [17]

The most improbable simulation for this coin is the heading when a coin is tossed 20 times will be 15.

<h3>What is probability?</h3>

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.