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2 years ago

Given a-2b=8, 4a+3b= 21; prove b= -1 please give a step by step answer

Mathematics

1 answer:

mixas84 [53]2 years ago

7 0

Answer:

Step-by-step explanation:

We can solve this with some pretty simple substitution

First write that a=2b+8

and our reasoning for this is that we added 2b from the first equation

Then write

4(2b+8)+3b=21

After we figured out what A was in the previous part we are able to substitute that into our other equation

Then you solve for b from here

8b+32+3b=21

11b=-11

b= -1

If you have any questions leave them below

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What is square root of the product of the number z and itself<br>

dsp73

Answer:

$\large\boxed{z}$

Step-by-step explanation:

What is square root of the product of the number z and itself?

Break down into smaller parts

What is the product of the number z and itself?

Product = multiply

Write an equation multiplying z by itself

z * z

Bring back the full question: What is the square root of the product of the number z and itself?

Now we can just add a $\sqrt{}$ to the front of our equation to solve the problem.

$\sqrt{z * z}$

Simplify

z * z = $z^{2}$

$\sqrt{z^{2} }$

In this case, the square root cancels out the exponent ( $z^{2}$ ), so $\sqrt{z^{2} }$ can simplify to z.

Hope this helps :)

8 0

2 years ago

A plant has an initial height of 3 inches and grows at a constant rate of 2 inches each month. A second plant that also grows at

Hitman42 [59]

Answer:

4.8 months

Step-by-step explanation:

First, let's write down the information that we are given.

Plant A:

Initial Height: 3 in.

Constant Rate of Growth (CRG): 2in/month (2 inches per month)

Plant B:

Initial Height: 1 in.

CRG: 29in/year (29 inches per year)

We can see that Plant B grows 29 inches per year, so lets convert Plant B's 'CGR' to months.

Plant B - Divide by 12 (12 months in a year)

29/12 in/year

Now, Lets put these into equations:

Plant A: y = 2x + 3

Plant B: y = 29/12 x + 1

Now, set these two equations together and solve for x.

2x + 3 = 29/12 x + 1

2 = 5/12 x

4.8

So, after 4.8 months, the plants will be the same height.

7 0

2 years ago

According to the synthetic division below, which of the following statements are true?

makkiz [27]

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

$2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.$

Therefore,

when $2x^2+9x-7$ is divided by $x+6,$ the remainder is 11 (option D is correct). To find the remainder after division by $x-6,$ you have to use another synthetic division. Actually, $2x^+9x-7=(x-6)(2x+21)+119,$ then the remainder is 119 (option C is false).
when $x=-6,$ the expression $x+6$ is $-6+6=0$ and $2x^2+9x-7=0\cdot (2x-3)+11=11$ (option A is correct). You cannot state the same when $x=6$ (option B is false).
neither $x-6$ nor $x+6$ is a factor of $2x^2+9x-7,$ because the remainders in both cases are not equal to 0 (options E and F are false).

4 0

2 years ago

Read 2 more answers

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

maksim [4K]

Answer:

Boat traveled 553.24 feet towards the lighthouse.

Step-by-step explanation:

In the figure attached AB is the light house of height 200 feet.

Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'

so 1' = $\frac{1}{60}$ degree

so angle of elevation at point C = 14 + $\frac{52}{60}$

So angle of elevation from C = (14 + 0.87) = 14.87°

Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + $\frac{10}{60}$ = 45.17°

Now we have to calculate the distance CD, traveled by the boat.

In ΔABC

tan14.87 = $\frac{200}{BC}$

0.2655 = $\frac{200}{BC}$

BC = $\frac{200}{0.26552}$

BC = 753.239 feet

Similarly in ΔABD

tan45.17 = $\frac{200}{BD}$

1 = $\frac{200}{BD}$

BD = 200 feet

So distance CD = BC - BD

CD = 753.239 - 200

= 553.24 feet

Therefore, Boat traveled 553.24 feet towards the lighthouse.

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2 years ago

Read 2 more answers

Compare the values of the 2s and 5s in 55,220

bagirrra123 [75]

The five digit number, 55,220 contains to 5's and two 2's. The 5's are in the ten thousand and one thousand columns. This means that one five represents 50,000 and the second represents 5, 000. The two's are in the hundreds and tens columns meaning one 2 represents 200 and the other 2 represents 20. In a direct comparison of these numbers the 5's equal 55,000 and the 2's equal 220.

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2 years ago