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3 years ago

Look at the picture............................

Mathematics

1 answer:

Lemur [1.5K]3 years ago

7 0

There was $135 in Roland's bank account after the two-month period.

Step-by-step explanation:

Step 1:

Roland out $180 in his account at the beginning of July. This reduced by 25% over the next two months.

We need to determine how much 25% of $180 is. To do so we convert 25% into a fraction and multiply with 180.

25% of $180 $=\frac{25}{100} (180)= 45.$

So an amount of $45 reduced over two months.

Step 2:

To calculate the money Roland has in his account after two months, we subtract the amount reduced from the amount of money in his account at the beginning of July.

The amount of money in his bank account after the two-month period $180-45= 135.$

So there was $135 in Roland's bank account after the two-month period.

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Find the vector equation of the line through the points (1, 2, −1) and (2, 4, 5). Is the point (−5, −10, −37) on this line?

pav-90 [236]

Answer:

(1+t, 2+2t, -1+6t); C is on this line.

Step-by-step explanation:

Let's find the vector equation of the line.

Given information:

Point A is (1, 2, -1)

Point B is (2, 4, 5)

Point C is (-5, -10, -37)

The difference between the two first given points (A, B) is:

B-A=(2, 4, 5)-(1, 2, -1)=(2-1, 4-2, 5-(-1))=(1, 2, 6) which is called the direction vector, so the equation is:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)=(1+t, 2+2t, -1+6t)

Now let's find if point C is on the line:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)-(1, 2, -1)=t*(1, 2, 6)

(-5-1, -10-2, -37+1)=t*(1, 2, 6)

(-6, -12, -36)=t*(1, 2, 6) from where we can obtain:

1*t=-6 --> t=-6

2*t=-12 --> t=-6

6*t=-36 --> t=-6

In conclusion, because from all the equations we obtained t=-6, then point C is on this line.

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3 years ago

Brayden adds 1/3 cup of flour into a mixture every 1/2 minutes. What is the rate, in cups per minutes, at which Brayden adds flo

monitta

Answer: 2/3 cups a minute

Step-by-step explanation: If Brayden is adding 1/3 cups of flour to the mixture every 1/2 minutes, you double the 1/2 minutes to get one minute and since you doubled the 1/2 minutes you must double the 1/3 getting 2/3 cups a minute.

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3 years ago

What is the answer for 4i over 3+7i

icang [17]

Answer:

see explanation

Step-by-step explanation:

given $\frac{4i}{3+7i}$

To rationalise multiply the numerator/denominator by the conjugate of the denominator

the conjugate of 3 + 7i is 3 - 7i, hence

$\frac{4i(3-7i)}{(3+7i)(3-7i)}$

distribute the numerator/denominator

= $\frac{12i-28i^2}{9-49i^2}$

[ note that i² = - 1 ]

= $\frac{12i+28}{9+49}$

= $\frac{28+12i}{58}$

= $\frac{28}{58}$ + $\frac{12}{58}$ i

= $\frac{14}{29}$ + $\frac{6}{29}$ i ← in standard form

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3 years ago

Victor needs to box 61 laptop computers for a shipment. If he can fit 9 laptops in each box, how many boxes does he need?

just olya [345]

Answer:

he would need 7 boxes

Step-by-step explanation:

61/9= 6 with a remainder of 7 therefore instead of 6 boxes you would need 7 to put the rest of the laptops in

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3 years ago

Multiple Choice

mihalych1998 [28]

Answer:

D is correct

Step-by-step explanation:

A graph of that sort will make a perfectly mirrored "V" shape, and with no offset, the bottom point will be on the y axis. This means that the first equation will intercept the y axis at zero, the second will intercept the y-axis at -15.

"A" may seem correct also, as the second graph will intercept the x-axis at -15, but it is not complete, as it will intercept that axis at +15 as well.

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2 years ago