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2 years ago

1. The ordered pair (-1, -1) is a solution of the system -4x + 2y = 2 and x + y = -2.

1 answer:

5 0

1: (-1,-1) is (x, y) to see if it is a solution, you would just plug in x and y and see if the equation is true.
-4 (-1) + 2(-1) = 2
4 + -2 = 2
2 = 2 CORRECT
So... plug in x and y in the second equation to Make sure it works for that one too.
-1 + -1 = -2
-2 = -2 CORRECT
So, yes. (-1,-1) is a solution to both equations.

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A photo is 4 inches by 6 inches. What is the area of the photo?

kolezko [41]

4 * 6 = 24
The answer is, the area of the whole photo is 24.
Hope this helped :)

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3 years ago

Please Help!!! I am totally lost!<br><br> Solve for x and find mangleABC.

kupik [55]

When something bisects an angle, it cuts that angle in half. This means that ray BD cuts angle ABC in half. Therefore, angle ABD, which is formed by cutting the angle in half, is equal to angle CBD, which is also formed by cutting the angle in half. Because of this, you have to set the equation equal to each other.

9x-18=5x+2

Combine like terms. Add 18 to both sides.

9x=5x+20

Combine like terms. Subtract 5x from both sides.

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Divide 4 on both sides.

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2 years ago

Jasmine bought 6.4 pounds of chewy candy from the local confectionary store. If she gave 2.06 pounds of the candy to her little

Tatiana [17]

The answer would be B. All you would do is subtract 6.4 - 2.06 and you would annex a zero after the four. Then you would get 4.34

8 0

2 years ago

1500 soldiers arrive at a training camp. A few soldiers desert the camp. The drill sergeants divide the remaining soldiers into

iren [92.7K]

Answer:

The number of deserters is 34.

Step-by-step explanation:

We have to calculate the number of desertors in a group of 1500 soldiers.

The sergeant divides in groups of different numbers and count the lefts over.

If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.

If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.

If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.

If he divide in groups of 11, there are three left over. We can test with the 2 numbers we stay:

$(1431-3)/11=1428/11=129.82\\\\(1466-3)/11=1463/11=133$

As only 1466 gives a possible result (no decimals), this is the amount of soldiers left.

The deserters are 34:

$D=1500-1466=34$

6 0

3 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

2 years ago