Find the volume of a rectangular box having width 4.2 ft, length 8.694 ft, and height 7.643 ft.

E Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options.

kozerog [31]

Answer:

6feet by 5feet by 4feet

7feet by 6feet by 4feet

8feet by 3feet by 7feet

7 0

2 years ago

Wich expression represent the sum of 59 and x

KIM [24]

I don't see the answers, but it would most likely be 59 + x.

7 0

3 years ago

A<br> Write the equation for<br> line that<br> passes through (1, 1) and (-1,7)

KengaRu [80]

Answer:y=-3x+4

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(1,1) and (-1,7).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=1.

Also, let's call the second point you gave, (-1,7), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=7.

Now, just plug the numbers into the formula for m above, like this:

m=

7 - 1

-1 - 1

or...

m=

6

-2

or...

m=-3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(1,1). When x of the line is 1, y of the line must be 1.

(-1,7). When x of the line is -1, y of the line must be 7.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (-1,7).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,1). y=mx+b or 1=-3 × 1+b, or solving for b: b=1-(-3)(1). b=4.

(-1,7). y=mx+b or 7=-3 × -1+b, or solving for b: b=7-(-3)(-1). b=4.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(1,1) and (-1,7)

is

y=-3x+4

8 0

3 years ago

Hi there! Sorry to bother you, but can someone help me out with this?

Rudik [331]

Problem 6

<h3>Answer: A) Conjecture</h3>

Explanation:

We can rule out choices B through D because they are valid items to use in any proof. A definition is a statement (or set of statements) set up in a logical fashion that is very clear and unambiguous. This means there cannot be any contradiction to the definition. An example of a definition is a line is defined by 2 points (aka a line goes through 2 points).

A postulate is a term that refers to a basic concept that doesn't need much proof to see why it's true. An example would be the segment addition postulate which says we can break up a segment into smaller pieces only to glue those pieces back together and get the original segment back.

A theorem is more rigorous involving items B and C to make a chain of statements leading from a hypothesis to a conclusion. You usually would see theorems in the form "if this, then that". Where "this" and "that" are logical statements of some kind. One theorem example is the SSS congruence theorem that says "if two triangles have three pairs of congruent corresponding sides, then the triangles are congruent". Chaining previously proven/established theorems is often done to form new theorems. So math builds on itself.

A conjecture is basically a guess. You cannot just blindly guess and have it be valid in a proof. You can have a hypothesis and have it lead to a conclusion (whether true or false) but simply blindly guessing isn't going to cut it. So that's why conjectures aren't a good idea in a proof.

==========================================================

Problem 7

<h3>Answer: Choice A) A theorem does not require proof</h3>

Explanation:

As mentioned in the section above (paragraph 3), a theorem does require proof. It's like having a friend come up to you and make a claim, only to not back it up at all. Do you trust your friend? What if they might be lying? Now consider that instead of a friend, but now it's some random stranger you just met.

Of course, they may not realize they are lying but it's always a good idea to verify any claim no matter how trivial. Math tries to be as impartial as possible to have every theorem require proof. Some proofs are a few lines long (we consider these trivial) while others take up many pages, if not an entire book, depending on the complexity of the theorem.

So that's why we can rule out choice B since it's a true statement. Choices C and D sort of repeat the ideas mentioned, just phrased in different ways. As mentioned earlier, a theorem is built from fundamental building blocks of various definitions and postulates and theorems. The term "axiom" is more or less the same as "postulate" (though with slight differences).

If you wanted to go for a statement that doesn't require proof, then you'd go for an axiom or postulate. Another example of such would be something like "if two straight lines intersect, then they intersect at exactly one point".

5 0

2 years ago

Please help me asap I will give brainliest or whatever you want

dangina [55]

Answer/Step-by-step explanation:

Part A:

$Key:\left[1 Adult = 4 Student]$