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3 years ago

Solve for x. Then solve for the angle with the arrow.

Mathematics

1 answer:

ira [324]3 years ago

5 0

Answer:

132°

Step-by-step explanation:

The sum of interior angles of a pentagon is 540°

We sum all the angles and equate to 540.

91°+125°+92°+3x-5+4x-8=540°

This implies that:

295°+7x=540

7x=540-295

7x=245

x=35

The given angle is 4x-8

Substitute x=35

$4(35) - 8 = 132$

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How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?

Alex73 [517]

The solution is 25% acid, which means 2.5 liters acid (10 x .25).
you need that 2.5 liters to be 10%, or 1/10th the total. 
the total would have to be 25 liters (2.5 x 10) so when you add to 10 to get 25 you get 15 liters. Hope I helped!

3 0

2 years ago

Read 2 more answers

We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c

Kisachek [45]

We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

$\frac{dT}{dt}=k(T-a)$

We now separate the time and the temperature variables as follows,

$\frac{dT}{T-a}=kdt$

Integrating both sides of the differential equation, we obtain;

$ln(T-a)=kt +c$

This natural logarithmic equation can be rewritten as;

$T-a=e^{kt +c}$

Applying the laws of exponents, we obtain,

$T-a=e^{kt}\times e^{c}$

$T-a=e^{c}e^{kt}$

We were given the initial conditions,

$T(0)=4$

Let us apply this condition to obtain;

$4-20=e^{c}e^{k(0)}$

$-16=e^{c}$

Now our equation, becomes

$T-a=-16e^{kt}$

or

$T=a-16e^{kt}$

When we substitute a=20,
we obtain,

$T=20-16e^{kt}$

b) We were also given that,

$T(5)=8$

Let us apply this condition again to find k.

$8=20-16e^{5k}$

This implied

$-12=-16e^{5k}$

$\frac{-12}{-16}=e^{5k}$

$\frac{3}{4}=e^{5k}$

We take logarithm to base e of both sides,

$ln(\frac{3}{4})=5k$

This implies that,

$\frac{ln(\frac{3}{4})}{5}=k$

$k=-0.2877$

After 15 minutes, the temperature will be,

$T=20-16e^{-0.2877\times 15}$

$T=20-0.21376$

$T=19.786$

After 15 minutes, the temperature is approximately 20°C

6 0

2 years ago

Find the slope of (-3,8)(5,-1)

Svetach [21]

Answer:

Step-by-step explanation:

(-1 - 8)/(5 + 3) = -9/8 is the slope

7 0

2 years ago

What times what equals 120 and adds up to 14

sesenic [268]

No solution; 14/2 = 7; 7^2 = 49; 49 < 120
the 2 numbers that add up to 14 that would give the largest product is less than 120
maybe you mean 120 is negative?
idk i might be wrong

3 0

2 years ago

A hardware store sells single digits to be used for house numbers. There are five 5s, four 4s, three 3s and two 2s available. Fr

Andrei [34K]

Since there are no restrictions on the three-digit numbers (for example no repetitions), we actually don't care about the values of the digits. All we need to know is that there are

$5+4+3+2 = 14$

possible digits, and that we have to extract a triplet from here.

For problems like this we have the binomial coefficient, defined as

$\displaystyle \binom{n}{k} = \dfrac{n!}{k!(n-k)!},\qquad 0\leq k \leq n$

This number tells you how many subsets of k elements you can extract from a set of n elements. So, in your case, you want to compute

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6 0

2 years ago