All categories

2 years ago

Find a solution to the following system of equations. –5x + y = –5 –4x + 2y = 2

1 answer:

8 0

-5x + y = -5.....multiply by -2
-4x + 2y = 2
---------------
10x - 2y = 10 (result of multiplying by -2)
-4x + 2y = 2
-----------------add
6x = 12
x = 12/6
x = 2

-5x + y = -5
-5(2) + y = -5
-10 + y = -5
y = -5 + 10
y = 5

solution is (2,5)

You might be interested in

Wildlife resort has eight elephant cabs born during the summer and now has 31 total how many elephants were ending was there bef

Kipish [7]

The answer would be 23. 31-8=23

4 0

3 years ago

A parallelogram has a length of 15cm and a height of 7.5cm . Calculate it’s area (step by step)

poizon [28]

Answer:

Area of parallelogram is equal to $112.5cm^2$

Step-by-step explanation:

It is given length pf parallelogram which is equal to base of parallelogram is b=15 cm

Height of parallelogram h = 7.5 cm

We have to find the area of the parallelogram.

Area of parallelogram is equal to multiplication of base and height.

Therefore area of parallelogram is,

$A=bh$ , here b is base and h is height.

So $A=15\times 7.5=112.5cm^2$

Therefore area of parallelogram is equal to $112.5cm^2$

3 0

2 years ago

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin

Tanya [424]

Let the coordinates of the treasure be (x,y).
Let $d_{1}$ = distance from the rock to the treasure.
Let $d_{2}$ = distance from the tree to the treasure.
$d_{1} = \sqrt{(x\2 + (y-2)^2}$
$d_{2} = \sqrt{(16-x)^2 + (21-y)^2}$
We want $\frac{ d_{1} }{ d_{2} }$ = 5/9 in order to locate the treasure.

Note that 5/9 = 0.556 (approx)
Test (11.4, 14.2)
d1 = 14.8, d2 = 8.2, d1/d2 = 1.8 Incorrect
Test (7.6, 8.8)
d1 = 8.2, d2 = 14.8, d1/d2 = 0.554 Correct
Test (5.7, 7.5)
d1 = 6.13, d2 = 16.98, d1/d2 = 0.36 Incorrect
Test (10.2, 12.6)
d1 = 12.8, d2 = 10.2, d1/d2 = 1.255 Incorrect

Answer: The correct answer is (7.6, 8.8)

4 0

2 years ago

Read 2 more answers

How do I find the slope of this altitude? I am referring to question 19.

Crazy boy [7]

The altitude's slope must be perpendicular to that of the line.

The slope of segment BC is 2/5. The slope of the altitude must be perpendicular to 2/5. Since the negative reciprocal of 2/5 is -5/2, then the slope of the altitude is -5/2.

6 0

2 years ago

Read 2 more answers

Solve for w, where w is a real number.

Ber [7]

Answer:

w= 9

Step-by-step explanation:

$\sqrt{ - 4w + 61} = w - 4$

Square both sides:

-4w +61= (w -4)²

$\boxed{(a - b)^{2} = a^2 -2ab + b^2 }$

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

6 0

2 years ago

Read 2 more answers