1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
USPshnik [31]
3 years ago
11

Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.

Mathematics
1 answer:
vlabodo [156]3 years ago
4 0

Answer:

Real numbers = 39 and 9

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0

Given the following data;

a = 1

b = -43

c = 306

Quadratic equation formula is;

x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a}

Substituting into the equation, we have;

x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1}

x = \frac {43 \pm \sqrt {1849 - 1224}}{2}

x = \frac {43 \pm \sqrt {625}}{2}

x = \frac {43 \pm 25}{2}

x_{1} = \frac {43 + 25}{2}

x_{1} = \frac {68}{2}

x_{1} = 39

x_{2} = \frac {43 - 25}{2}

x_{2} = \frac {18}{2}

x_{2} = 9

Therefore, the two real numbers are 39 and 9.

The quadratic equation now becomes;

x² - 43x + 306 = (x - 39)(x - 9) = 0

You might be interested in
Jeff has 4 red pens and 2 blue pens in his backpack. He also has 1 yellow highlighter and 4 green highlighters in his
Romashka-Z-Leto [24]

Answer:

\frac{1}{15}

Step-by-step explanation:

In probability,

"AND" means "multiplication"

"OR" means "ADDITION"

We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.

Let P(b) be probability of blue pen

Let P(y) be probability of yellow highlighter

We know probability of event is that event divided by total number of that

So,

There are 4 + 2 = 6 pens

Blue pen = 2

Hence,

P(b) = 2/6 = 1/3

And,

There are 5 highlighters

Yellow highlighter = 1

Hence,

P(y) = 1/5

Now,

P(b and y) = 1/3 * 1/5 = 1/15

Hence,

probability of grabbing blue pen and a yellow highlighter is  \frac{1}{15}

3 0
3 years ago
Read 2 more answers
Can you please help thanks
katrin2010 [14]

Answer:5/2a + 10/3b

Step-by-step explanation:

(1/6)(15a+20b)

=(1/6)(15a)+(1/6)(20b)

6 0
2 years ago
3.1 = x / 2 equals what?
neonofarm [45]

Answer: 6.2

Step-by-step explanation: 3.1 = x/2

x/2=3.1

x/2(2)=3.1(2)

x=6.2

3 0
2 years ago
Working simultaneously, four fudge machines complete a big order in 32 hours. All the machines at the fudge factory work at the
Alinara [238K]

Answer:

4 Hours

Step-by-step explanation:

Let's say that the rate of the machines 1/x, because every time they complete an order, it takes them x hours. To find x, we have to add the the rates of the individual machines, which would equal the rate of the machines working together. We know that there are four machines working together at the same rate, and it took them 32 hours.

So:

1/x + 1/x + 1/x + 1/x = 1/32

1/4x = 1/32

4x = 32

x = 8

Thus, the rate of the machines is 1/8.

Now we have to find the time of the order with only half of the machines working together. This time, we don't know the combined rate, so I'll substitute it for y.

1/8 + 1/8 = 1/y

1/4 = 1/y

y = 4

The time taken to complete it is 4 hours.  

3 0
2 years ago
Read 2 more answers
I am a number between 10 and 25. I am a multiple of 8 and one of my digits is 2 what number am I?
zalisa [80]
24 could be it................
7 0
3 years ago
Read 2 more answers
Other questions:
  • Gina's number is 2 more than sara's. the sum of their numbers is 68. what are their numbers?
    14·2 answers
  • Find The Distance Between (6,1) and (-2,-4)
    7·1 answer
  • Common denominators for 5/6 and 8/21 help me!!!!!!!!!
    11·1 answer
  • A pizza was divide
    14·2 answers
  • each morning a gardener uses 24 3/4 gallons of water from a barrel. each afternoon, she adds 15 1/4 gallons of water to the barr
    12·1 answer
  • Assume that during each second, a job arrives at a webserver with probability 0.03. Use the Poisson distribution to estimate the
    15·1 answer
  • Find the range of the function f(x)=x2+5 given the domain (-2,-1,0,1,2)?
    15·1 answer
  • Write 2 quadratic equations that are NOT equivalent, each forming a graph with X-
    14·1 answer
  • Gordon types 3,724 words in 49 minutes. Find the unit rate. Gordon types words per minute. ​
    10·1 answer
  • Where would
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!