Simplify the sum: (5u^3+7u^2+7)+(7u^3-6u+5)

Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).

lawyer [7]

x = 4

because it is perpendicular, the new equation has to be a vertical since the original was horizontal. We know that it passes through (4,-2) so it has to be x=4

4 0

3 years ago

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A culture started with 5,000 bacteria. After 2 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after

lesya [120]

This can be expressed as exponential growth of the form:

f=ir^t, f=final amount, i=initial amount, r=common ratio (rate), t=time

In this case we are given the point (2, 6500) and i=5000 so we can solve for the rate...

6500=5000r^2 divide both sides by 5000

1.3=r^2 take the square root of both sides and note that we know r>0

r=1.3^(1/2) so our equation becomes:

f=5000(1.3)^(1/2)^t and knowing that (a^b)^c=a^(b*c) we can say:

f=5000(1.3)^(t/2) so for t=18

f=5000(1.3)^9

f≈53022 (to nearest whole bacteria)

7 0

3 years ago

Given: TSR and QRS are right angles; T ≅ Q

allsm [11]

Answer:

The answer is number (2) ⇒ because of the AAS congruence theorem

Step-by-step explanation:

* Lets use the information to solve the problem

- In the given triangles TSR and QRS

# We have a common side RS or SR

# Two right angles TSR and QRS

# m∠T = m∠Q ⇒ given

* So we have two pairs of angles and one common side, lets

revise the cases of congruence

- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

and one side in the 2ndΔ

* Now lets read the statements and write the missing

Step 1: m∠TSR = m∠QRS = 90° ⇒ because all right angles are congruent

Step 2: m∠T = m∠Q ⇒ because it is given

Step 3: SR ≅ RS ⇒ because of reflexive property (common side)

Step 4: Δ TSR ≅ ΔQRS ⇒ because of the AAS congruence theorem

* The answer is number (2)

4 0

3 years ago

Read 2 more answers

Helpp please!!!

zavuch27 [327]

Answer:

h, j2, f, g, j1, i, k, l (ell)

Step-by-step explanation:

The horizontal asymptote is the constant term of the quotient of the numerator and denominator functions. Generally, it it is the coefficient of the ratio of the highest-degree terms (when they have the same degree). It is zero if the denominator has a higher degree (as for function f(x)).

We note there are two functions named j(x). The one appearing second from the top of the list we'll call j1(x); the one third from the bottom we'll call j2(x).

The horizontal asymptotes are ...

h(x): 16x/(-4x) = -4
j1(x): 2x^2/x^2 = 2
i(x): 3x/x = 3
l(x): 15x/(2x) = 7.5
g(x): x^2/x^2 = 1
j2(x): 3x^2/-x^2 = -3
f(x): 0x^2/(12x^2) = 0
k(x): 5x^2/x^2 = 5

So, the ordering least-to-greatest is ...

h (-4), j2 (-3), f (0), g (1), j1 (2), i (3), k (5), l (7.5)

6 0

3 years ago

The width of a rectangle is 2 less than its length. If the perimeter of the rectangle is no more than30 centimeters, find the ra

arlik [135]

If this is what u are asking for 240 is what i got for the answer

4 0

3 years ago