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-BARSIC- [3]
3 years ago
13

Five times a number minus eight is the same as ten more than three times a number. Find the number.

Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

Answer:

25

Step-by-step explanation:

5(n-8)=3n+10

5n-40=3n+10

5n=3n+50

2n=50

n=25

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
zlopas [31]
<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

5 0
3 years ago
2x - 2y = 10 and x + 2y = 11
Rufina [12.5K]

Answer:

Step-by-step explanation:

What are u asking for x or y

7 0
3 years ago
Find the sum and express it in simplest form. (ab+4a-6)+(ab+6)
riadik2000 [5.3K]
= 2ab + 4a + 6 - 6

= 2ab + 4a

you can factor this  to 2a(b + 2)
3 0
3 years ago
Read 2 more answers
Find a point-slope form for the line with slope 1/5 and passing through the point (-4,-9).
sattari [20]

Answer:

y + 9 = \frac{1}{5}(x + 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = \frac{1}{5} and (a, b) = (- 4, - 9) , thus

y - (- 9) = \frac{1}{5}(x - (- 4) ) , that is

y + 9 = \frac{1}{5}(x + 4)

3 0
2 years ago
Convert 0xBAD into a decimal number
hammer [34]
0xBAD = 2989
Hope I helped.
7 0
3 years ago
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