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
nadya68 [22]
2 years ago
5

How many real solutions exist for this system of equations?

Mathematics
1 answer:
Rom4ik [11]2 years ago
7 0

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

{x}^{2}  + 4 = 4x

{x}^{2}  - 4x + 4

Find the discrimant.

{ - 4 {}^{2} - 4(1)(4) } = 0

This means there is one real solution. Since the discramnt equal 0.

You might be interested in
Select the statements that are true based on the following given information. D = {x | x is a whole number} E = {x | x is a perf
likoan [24]
<h3>2 Answers: Choice C and Choice D</h3>

==========================================================

Explanation:

Let's write the roster notation of each set

D = {0, 1, 2, 3, ...} the dots indicate the pattern goes on forever

E = {0, 1, 4, 9, 16, 25} = list of perfect squares smaller than 36

F = {20, 22, 24, 26, 28, 30} = even numbers between 20 and 30

----------------

If we intersect sets D and E, we're looking for what numbers are in both sets at the same time. Therefore, D ∩ E = {0, 1, 4, 9, 16, 25} which is the exact same as set E. This is because all of set E is inside of set D. We say that set E is a subset of set D. So, D ∩ E = E.

Choice A is very close to being true. The problem is that 25 is missing from the set {1,4,9,16}. So this is why choice A is false.

----------------

Now let's intersect sets D and F. The numbers they have in common are {20, 22, 24, 26, 28, 30} which is exactly what set F is. So set F is a subset of set D. We can write D ∩ F = F in much the same way we can say D ∩ E = E.

D ∩ F = {12,14,16,18} is not true. A number like 12 is not between 20 and 30, so it cannot be in set F.

Choice B is false so we cross it off the list.

----------------

Choice C is true and here's why

D ∪ (E ∩ F) is the same as saying D ∪ G where G is the set of intersecting E and F together. In other words, G = E ∩ F

We don't really need to even worry about sets E, F or G. All that matters here is set D.

When we write D ∪ (E ∩ F) or D ∪ G, we're saying "a number is in set D, or it is in set G". If it is in D, then it's a whole number. Otherwise, it's in a subset of whole numbers.

Overall, D ∪ G and D ∪ (E ∩ F) form the entire set of whole numbers.

------------------

Choice D is true.

E and F have nothing in common

E = {0, 1, 4, 9, 16, 25}

F = {20, 22, 24, 26, 28, 30}

So intersecting them leads to the empty set. This is the set with nothing inside it, not even 0.

------------------

Choice F is false

These two sets below

E = {0, 1, 4, 9, 16, 25}

F = {20, 22, 24, 26, 28, 30}

union together to get

H = {0,1,4,9,16,20,22,24,25,26,28,30}

just toss all of the numbers together into one big set

Notice how each of these numbers are whole numbers, so they are part of set D. This means set H is also a subset of set D.

When we intersect sets D and H, we end up with set H. We do not simply end up with the set with 25 only inside it.

6 0
3 years ago
What does it mean if y values is the same
solong [7]
If their equal(Same amount)
3 0
3 years ago
Read 2 more answers
Jade can do 65 push ups in 5 minutes. At the same rate, how many push ups can you expect her to do in 7 minutes?
hram777 [196]

Answer:

91

Step-by-step explanation:

Set up a proportion, where x is the number of push ups she can do in 7 minutes

\frac{65}{5} = \frac{x}{7}

Cross multiply and solve for x:

5x = 455

x = 91

So, Jade can do 91 push ups in 7 minutes

3 0
3 years ago
Read 2 more answers
How do u put 72 7/10 into decimal?
NNADVOKAT [17]

Answer:

72.7

Step-by-step explanation:

First multiply 72 by 10

because 72 is 72 10s, making it a whole number.

then add 720 (72 times 10) to 7.

then all of that over 10.

then just divide.

727/10

72.7

this is what you do for all mixed numbers like that one.

7 0
2 years ago
Read 2 more answers
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the dista
Kamila [148]

40mph for Car B I think. 45mph for Car A. 45(mph) times 4(h) is 180(distance) and 40 times 4.5 is also 180. Sorry if I'm wrong.

8 0
3 years ago
Other questions:
  • Why was the baby any confused ?
    12·1 answer
  • Can someone explain y-intercept? I had a test, and I am pretty sure I bombed it. I really need help!!
    14·2 answers
  • Find the midpoint of the line segment with end coordinates of:(−2,−4) and (2,−10)
    9·1 answer
  • Can someone help me with 4?
    5·2 answers
  • Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represen
    10·1 answer
  • Simplify 3(x - 6) - 4(x 3). <br> a. -x - 30 <br> b. -x - 9 <br> c. -x - 6 <br> d. -x2 - 30
    11·2 answers
  • How many solutions does the system have?
    14·2 answers
  • (please help!) <br> What is the length of AD?<br><br> AD=__
    10·1 answer
  • Round 0.0851 to the nearest whole number
    9·1 answer
  • PLEASE HURRY 50 POINTS AND I WILL VOTE U BRAINLY
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!