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bixtya [17]
3 years ago
8

What is the solution of the following system of equations? 2x + y = -7 -3x - 2y = 10

Mathematics
1 answer:
pentagon [3]3 years ago
8 0

Answer:

the solution is    (-4, -3)

Step-by-step explanation:

Multiply the first equation by 2.  This produces 4x + 2y = -14.

Now combine this result with the second equation:

4x + 2y = -14

-3x - 2y = 10

------------------

 x          = -4

Subbing -4 for x in the first equation yields 2x - 4 = -7, or 2x = -3.  

Then x = -3/2, and the solution is    (-4, -3)

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Three forces act on a hook. Determine the magnitude of the resultant of the force.
Novay_Z [31]

Use Hooke's law... (just kidding)

Break down each force vector into horizontal and vertical components.

\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y

\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y

\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y

The resultant force is the sum of these vectors,

\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y

and has magnitude

|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N

The closest answer is D.

5 0
3 years ago
for every 5 coins carmen gets, she gives 2 to her brother Frankie. If carmen has 9 coins, how many does frankie have?
aliya0001 [1]
Since Carmen gives two coins to Frankie for every five that she gets, she effectively only gains 3 coins at a time. Therefore, if she has 9 coins, Frankie must have 6.
7 0
4 years ago
Ma.clark spends $89.85 on science kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?
k0ka [10]
The answer to this question is 17
8 0
3 years ago
Read 2 more answers
In 2000, the population of Massachusetts
Zepler [3.9K]

Answer:

The population reaches 7 million people in the year 2032.

Step-by-step explanation:

We have that

f(x) = 6.3*(1.0032)^{x}

Using this model, find the year when the population reaches 7 million people.

This is x years after 2000, in which x is found when f(x) = 7. So

f(x) = 6.3*(1.0032)^{x}

7 = 6.3*(1.0032)^{x}

(1.0032)^{x} = \frac{7}{6.3}

(1.0032)^{x} = 1.11

We have to following logarithm rule

\log{a^{x}} = x\log{a}

So we apply log to both sides of the equality

\log{(1.0032)^{x}} = \log{1.11}

x\log{1.0032} = \log{1.11}

x = \frac{\log{1.11}}{\log{1.0032}}

x = 32.66

2000 + 32.66 = 2032

The population reaches 7 million people in the year 2032.

3 0
3 years ago
And angle measures 54° more than the measure of its complementary angle what is the measure of each angle
Mashutka [201]
Answer:
The measure of the angles are 72 degrees and 18 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x -----> the measure of an angle
y-----> the measure of he other angle
we know that
x+y=90 -----> y=90-x -----> equation A
x=y+54 ----> equation B
substitute equation B in equation A and solve for y
y=90-(y+54)
y=90-y-54
2y=36
y=18°
Find the value of x
x=y+54 -----> x=18+54=72°
therefore
The measure of the angles are 72 degrees and 18 degrees
4 0
3 years ago
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