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3 years ago

Do you think there are any ordered pairs that are solutions to BOTH y = x + 5 and y = –2x – 1? Explain.

Mathematics

2 answers:

zloy xaker [14]3 years ago

8 0

Answer:

The ordered pair is $(-2,3)$

Step-by-step explanation:

$y=x+5\\y=-2x-1\\\implies x+5=-2x-1\\\implies 3x=-6\\\boxed{x=-2}\\\implies y=-2+5=\boxed {3}\\$

makkiz [27]3 years ago

3 0

Answer:

(-2,3)

Step-by-step explanation:

Set the two equations equal to each other since they both equal y

x + 5 = -2x - 1

+2x +2x Add 2x to both sides

3x + 5 = -1

- 5 - 5 Subtract 5 from both sides

3x = -6 Divide both sides by 3

x = -2

Plug this into one of the original equations

y = x + 5

y = -2 + 5 Add

y = 3

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Determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5. Justify your answer.

Rudik [331]

Step-by-step explanation:

Given

The function is $f(x)=x+4$

for $x_2>x_1$ , we will check the values of $f(x_1)$ and $f(x_2)$

Take 3 and 4

$f(4)=4+4\\f(4)=8$

Similarly,

$f(3)=3+4\\f(3)=7$

Thus, $f(4)>f(3)$

Also, $f'(x)$ is 1 i.e. a constant value. So, the function is increasing linearly for the given interval.

7 0

3 years ago

Two students, Ann and Max, factored the trinomial 4x2-6x -4. Ann factored it as 2(k 2xx+ 1) and Max factored it as (-2)4x+2), In

marishachu [46]

Given trinomial 4x^2-6x-4.

In order to factor a trinomial, we need to factor out greatest common factor (GCF).

In the given trinomial, we have terms 4x^2, -6x, -4.

We can see that all terms can be divided by a greatest number 2.

Therefore, greatest common factor would be 2 there.

We need to factor out 2 first.

On factoring out 2, we get

2(2x^2 -3x -2).

Now, we need to factor out trinomial 2x^2 -3x -2 now.

We can factor a trinomial by applying product sum rule.

We have a=2,b=-3,c=-2.

ac= 2*-2 = -4 and b=-3.

So, we need to find the factors of -4 that add upto -3.

Factors of -4 would be -4 and 1.

Let us replace -3x by -4x +1x in 2x^2 -3x -2 trinomial

2x^2 -3x -2 could be rewrite as 2x^2 -4x +1x -2.

Making it into two groups and factoring out GCF of each group.

We get

(2x^2 -4x) +(1x - 2)

2x(x-2) +1(x-2)

=(x-2)(2x+1)

Therefore, final factors of the trinomial is 2(x-2)(2x+1).

So, Ann factored form 2(x-2)(2x+1) is correct.

8 0

3 years ago

Can a pentagon have angles that measure 95°, 67°, 105°, 95°, and 177°?

pochemuha

Answer:

No, it cannot have angles that measure 95°, 67°, 105°, 95°, and 177°.

Step-by-step explanation:

S = (n-2) * 180

A pentagon has 5 sides, so substitute n for sides (n = 5)

s = 5-2) * 180 = 540°

95° + 67° + 105° + 95° + 177° = 539°

Hope that Helps!

7 0

3 years ago

Translate this sentence into an algebraic equation.

oksano4ka [1.4K]

Answer:

$\boxed{\bold{5y-8=16}}$

Step By Step Explanation:

Vocabulary:

Product Of: Multiplication

Less Than: Subtraction

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

Pick Apart The Sentence:

8 Less Than: Eight Is Being Subtracted From A Number

The Product Of 5 And y: 5 And y Are Being Multiplied Together

Is 16: The Final Result Is 16

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

Piece Together:

5y - 8 = 16

5 and y are bing multiplied, then 8 is being subtracted from that. The final result is 16.

- Mordancy

4 0

3 years ago

Read 2 more answers

The number of bacteria in a culture increases continuously and rapidly when put under a heat source. a culture containing 20 bac

Len [333]

Answer:

The answer is 14.46%

Step-by-step explanation:

Given is : A culture containing 20 bacteria multiplies to 117,360 in one minute.

Let A0 be initial bacteria count = 20

Let A be final bacteria count = 117360

Time = 60 seconds

R = rate

Formula to be used = $A=A0e^{rt}$

$117360=20e^{r*60}$

$5868=e^{60r}$

Taking log function (ln) on both sides.

$ln(5868)=ln(e^{60r} )$

$60r=8.677$

Hence, r = 0.1446 and in percentage it is 14.46%

5 0

3 years ago