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3 years ago

How to solve 5a + c = -8a

Mathematics

1 answer:

sergey [27]3 years ago

6 0

Solve for a:

$5a+c=-8a\ \ \ |-c\\\\5a=-8a-c\ \ \ |+8a\\\\13a=-c\ \ \ |:13\\\\\boxed{a=-\dfrac{c}{13}}$

Solve for c:

$5a+c=-8a\ \ \ \ |-5a\\\\\boxed{c=-13a}$

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In the past month, Kaitlin rented 1 video game and 4 DVDs. The rental price for the video game was $2.40 The rental price for ea

vichka [17]

Answer:

$2.40 for the video game and $14.8 for the DVDs

Step-by-step explanation:

1 video game = $2.40

4 DVDs = $14.8

$3.70 x 4 = $14.8

6 0

3 years ago

Kylie explained that (–4x + 9)2 will result in a difference of squares because (–4x + 9)2 = (–4x)2 + (9)2 = 16x2 + 81. Which sta

Serjik [45]

The correct product should have been:
(–4x + 9)2 = (-4x)2 + 2(-4x)(9) + 9^2 = 16x6 - 72x +81
The result is a trinomial and not a binomial nor a difference of two squares.

So, the answer is:
C = Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.

8 0

3 years ago

Read 2 more answers

At 1:30 p.m., Tom leaves in his boat from a dock and heads south. He travels at a rate of 25 miles per hour. Ten minutes later,

Nadya [2.5K]

Answer: she would catch up with Tom in 1 hour.

Step-by-step explanation:

Let t represent the time it will take for Mary to catch up with Tom.

Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.

Distance = speed × time

Distance travelled by Tom in t hours is

25 × t = 25t

Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour

Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in

(t - 10/60) hours is

30(t - 10/60)

= 30t - 5

By the time she catches up with Tom, they would have covered the same distance. It means that

25t = 30t - 5

30t - 25t = 5

5t = 5

t = 5/5 = 1 hour

7 0

3 years ago

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

pochemuha

Answer:

The quadratic function whose graph contains these points is $y=-x^{2}-2x-2$

Step-by-step explanation:

We know that a quadratic function is a function of the form $y=ax^{2}+bx+c$ . The first step is use the 3 points given to write 3 equations to find the values of the constants a,b, and c.

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

$-2=a*0^{2}+b*0+c\\c=-2$

$-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17$

$-17=a*3^{2}+b*3+c\\ c=-9a-3b-17$

We can solve these system of equations by substitution

Substitute $c=-9a-3b-17$

$-9a-3b-17=25a+5b-17\\-9a-3b-17=-2$

Isolate a for the first equation

$-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}$

Substitute $a=\frac{b}{2}$ into the second equation

$-9\left(-\frac{b}{2}\right)-3b-17=-2$

Find the value of b

$-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2$

Find the value of a

$a=\frac{b}{2}\\ a=-1$

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

$y=-x^{2}-2x-2$

As you can corroborate with the graph of this function.

8 0

3 years ago

I rent a gym for $200.00 for 30 students. A year later I rent the gym for $330 for 70 students.

Anna [14]

let X be number of students

and y be total cost

when 30 students (30,X)where at the gym it's costs 200 (y,200)

=that is (X,y)=(30,200)

when 70 students where at the gym

=(X,y)= (70,330)

now we find the slope

M=y2-y1/x2-x1

= 330-200/70-30

= 100/40

= 2.5=3

now

Y=Mx+b

Y=2x+b

we need to find the value of b

so,we substrate for X and Y

X=30,200

200=2(30)+b

re-arrange

B+60=200

B=200-60

=140

y=2x+140

For the other questions, I can look at the equation I got. The y-intercept (b value) is $200. That means that we are adding $200 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.

hope it's helpful

and please I really need brainliest, thanks

7 0

2 years ago