All categories

3 years ago

(look at image) can i get help with these two?

Mathematics

1 answer:

serg [7]3 years ago

6 0

Answer:

1. x = 2, AC = 30, AB - 4

2. y = 4, AB = 34, BC = 34

Step-by-step explanation:

1. AB + BC = AC so 26 + (10 - 3x) = 14x +2 and then add 3x to both sides and subtract 2 from both sides to get x on one side and an integer on the other side which is 34 = 17x and then divide 17 from both sides to get x = 2 and then substitute x into the AC and AB equations to find the values its equal to.

2. The symbol in the given means that the two lengths are congruent which means they are equal to each other so you put the two equations equal to each other and solve for y. 9y -2 = 14 + 5y, so subtract 5y from both sides and add two to both sides to get 4y = 16 and then divide both sides by 4 to get y = 4 and then substitute in the answer to find the lengths of AB and BC.

You might be interested in

Which expression is equivalent to 13 - -21

Ber [7]

13 + 21 = 13- -21

The minus sign and negative cancel each other out.

5 0

3 years ago

Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}

Deffense [45]

Start with a line segment connecting two points, A and B. $\dfrac{DA}{BA}=3$ means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with $\dfrac{DB}{BA}=2$ , or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, $\dfrac{AB}{CB}=\dfrac12$ , so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let $d$ be the length of AB. Then the length of CD in terms of $d$ is $4d$ . We have the coordinates of C and D, and the distance between them is $\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2$ . So

$4d=4\sqrt2\implies d=\sqrt2$

The slope of the line through C and D is

$\dfrac{0-4}{4-0}=-1$

and so the equation of the line through these points is

$y-4=-(x-0)\implies x+y=4$

So the coordinates of A are $(x,y)=(x,4-x)$ . The distance between C and A is $d=\sqrt2$ , so we have

$\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1$

Since A falls to the right of C (in the $x,y$ plane, not just in the sketch), we know to take the positive value $x=1$ . Then the $y$ coordinate is $y=4-1=3$ .

All this to say that A is the point (1, 3), so

$2x+y=2+3=5$

5 0

3 years ago

What is the definition of a line

kolezko [41]

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

3 0

3 years ago

Read 2 more answers

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find the length of AC.

Oxana [17]

Answer:

AC=16 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. It was given that diagonals AC and BD intersect at point E.

This implies that: $AE=CE$ .

We substitute the expression for x, we get:

$11x-3=12-4x$ .

Group similar terms to get:

$11x+4x=12+3$ .

$15x=15$ .

$x=1$

AC = 2(12-4x)

AC=2(12-4(1))

AC=2(8)

AC=16

8 0

3 years ago

The figure shows a triangle with its three angle bisectors intersecting at Point P.

NeX [460]

Check the picture below.

we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangle FPZ and triangle FPY are both congruent, so their sides are also congruents, thus PY = PZ.

7 0

2 years ago