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2 years ago

Which of the following is a factor of 2xy + 8y − 8x − 32?

Mathematics

1 answer:

jok3333 [9.3K]2 years ago

7 0

The correct factorization of this equation is (2y - 8)(x + 4).

In order to factor polynomials with 4 terms like this, you can often use a strategy called grouping. To do that, split into two different binomials.

(2xy + 8y) and (-8x - 32)

Now you can factor out the greatest common factor of each parenthesis.

2y(x + 4) and -8(x + 4)

Now in grouping, if after factoring out the greatest common factor, you can put the two things you pulled out in one parenthesis. You can multiply that by one of the matching set for the final answer.

(2y - 8)(x + 4)

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If y=e5t is a solution to the differential equation

a_sh-v [17]

Answer:

k = 30, $y(t) = C_1e^{5t}+C_2e^{6t}$

Step-by-step explanation:

Since $y=e^{5t}$ is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

$\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}$

Then, replacing the derivatives in the equation we have:

$25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0$

Since $e^{5t}$ is a positive function, we have that

$25-55+k = 0 \rightarrow k = 30$ .

Now, consider a general solution $y(t) = Ae^{rt}, A \in \mathbb{R}$ , then, by calculating the derivatives and replacing them in the equation, we get

$Ae^{rt}(r^2-11r+30)=0$

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

$y(t) = C_1e^{5t}+C_2e^{6t}$

8 0

3 years ago

rove the following statement directly from the definition of rational number. The difference of any two rational numbers is a ra

Umnica [9.8K]

Answer:

Step-by-step explanation:

Question:

Prove the following statement directly from the definitions.

The difference of any two rational numbers is a rational number.

Answer, see attachment for proof.

7 0

2 years ago

PLEASE HELP ME ANWSER THISSS

Lera25 [3.4K]

Answer:

Step-by-step explanation:

Find the measure of the vertex angle ∠ABD of an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem

∠ABD=∠BAD= ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD= ------> the sum of the internal angles of a triangle is equal to

Step 2

Find the measure of the angle ∠CBD in the equilateral triangle

we know that

A equilateral triangle has three equal sides and three equal angles

The measure of the internal angle in a equilateral triangle is

∠CBD=

Step 3

Find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC=

therefore

the answer is

the measure of the angle ∠ABC is

6 0

2 years ago

The members of the basketball team ordered 5 tuna sandwiches at $3.99 each, 5 fish tacos at $2.75 each, 3 salads at $2.70 each,

Oliga [24]

Firstly, $3.99 × 5 = $19.95

Second, $2.75 × 5 = $13.75

Third, $2.70 × 3 = $8.1 (Since it is just $8.1 that won't make sense so we'd add a 0 so It's $8.10.)

Then we do the last one which is 13 × $0.89 = $11.57.

So now since we are done multiplying we can add it all up.

The answer is $53.37 when we finish adding it up.

and I don't know what A number sentence is sorry :(

I took a long time typing this :< I hope this helps though! :D

7 0

2 years ago

Can someone see and answer this

Natasha_Volkova [10]

Answer:

I can’t see the picture well please make it more detailed

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers