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3 years ago

Anyone know the answer and the check to the equation 7 - 4c = 3c - 7 ?

Mathematics

2 answers:

givi [52]3 years ago

8 0

Answer:

c= 2

Step-by-step explanation:

7 - 4c = 3c - 7

Add 4c to both sides

7 = 7c - 7

Add 7 to both sides

14 = 7c

Divide both sides by 7

2 = c

Gelneren [198K]3 years ago

3 0

Answer:

c=2

Step-by-step explanation:

7-4c=3c-7

7+7=3c+4c

14=7c

Dividing both sides by 7

c=2

CHECK:

Putting c in the above equation

7-4(2)=3(2)-7

7-8=6-7

-1=-1

Hence the above solution satisfies the given equation

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5 0

3 years ago

Please help! Thanks in advance.

alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
$2 - 5 - 14 + a + b = 0$
$- 17 + a + b = 0$
$a + b = 17$

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
$2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0$
$512 - 320 - 224 + 4a + b = 0$
$- 32 + 4a + b = 0$
$4a + b = 32$

Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
$3a = 15$

Simplify:
$a = 5$

Now we have a, we can plug in one of those equations to find b:
$5 + b = 17$
$b = 17 - 5$
$b = 12$

So, the answers are $a=5$ and $b=12$ .