It is known that solve for the value of x algebraically.

Mathematics

1 answer:

otez555 [7]3 years ago

7 0

Answer:

x + 3 = 9 (original equation )

x = 9 – 3 (take the constant term to the other side so that the variable x is isolated.)

x = 6

So x = 6 is the required solution to the equation.

Step-by-step explanation:

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Max was on vacation twice as long is Jared and half as long as Wesley. The boys were on vacation a total of three weeks. How man

nasty-shy [4]

To begin with, the question is asking for the answer in days, so let's change 3 weeks to days. There are 7 days in 1 week; 3 weeks times 7 days = 21 days.
21 total days of vacation.

Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)

M + J + W = 21 [This is the equation we'll be coming back to]

Now, we can use the clues given in the question to have an equation for each variable/boy.

Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.

So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W

To have an equation for each individual boy, we must rearrange the last two equations in the list.

First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J

Second, M = (1/2)W
Multiply both sides by 2
2M = W

New equations:
M + J + W = 21 [From the old list]
J = (1/2)W
W = 2M

Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
(7/2)M = 21

Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
$(\frac{2}{7})* (\frac{7}{2}m)= (\frac{2}{7})*(21)$
M = 6

Now we know Max was on vacation for 6 days.

If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.

So...
J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days

Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.

Let's double check our answer:
M + J + W = 21 days6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!

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3 years ago

You think that the distance between your house in a friends house is 5.5 miles the actual distance is 4.75 miles what is the per

fredd [130]

Its about 13.64% multiply 4.75 by 100 then divide by 5.5 then subtract that number from 100

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3 years ago

5. Each pair of polygons below are similar. Show your work! Solve for x:

Stella [2.4K]

Since they are similar, you need to find the ratio of similarity (I made up the term, there is probably a correct one that I can’t remember).

If you divide 16/40, you’ll find that that ratio is 2.5. So then you just multiply 16 x 2.5. You’ll get 18.

18 is the length of the top of the trapezoid.

You set 18=2x+4 and solve it algebraically. Subtract 4 from both sides.

14=2x
Divide by 2 and x=7

(You can also check that the ratio is right by 16/18 is the same decimal value as 40/45. You’ll get .88888...)

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3 years ago

In geometry, how do defined terms and undefined terms relate to each other

inysia [295]

In geometry, how do defined terms and undefined terms relate to each other?
Ask for details Follow Report by Da5ncing4bearnelogi 05.08.2016AnswersHussain514 AmbitiousIn geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane.

POINT (an undefined term)
In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y).

LINE (an undefined term)
In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them.

PLANE (an undefined term)
In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC).

Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point.

Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.

Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle.

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2 years ago

Glenn rolls a 6-sided die. What is the probability that he gets a number greater than 2 or an odd number?

Marysya12 [62]

Hello!

You can write down what the possible numbers their are

The numbers greater than 2 are 3, 4, 5, and 6

The numbers that are odd are 1, 3, and 5

List all the numbers out in a row

3, 4, 5, 6, 1, 3, 5,

Eliminate one of the numbers that repeat

3, 4, 5, 6, 1

You put the amount of answers of the total amount of outcomes

The answer is 5/6

Hope this helps!

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3 years ago