What is the Circumference of the circle with rounded to the nearest hundredth??

Find two positive real numbers whose product is a maximum. the sum of the first and three times the second is 60.

maksim [4K]

P = f*s
f +3s = 60

p = (60 -3s)*s = 3(20 -s)*s

This equation describes a parabola that opens downward. The roots of the equation are s=0 and s=20, so the axis of symmetry is s=(0+20)/2 = 10. That is, the vertex (maximum) will be found at s=10.

The second number is 10. The first number is 60-3*10 = 30.

The product is maximized when the first number is 30 and the second is 10.

4 0

3 years ago

If each quadrilateral below is a parallelogram, find the missing measures.

prisoha [69]

Step-by-step explanation:

We will use parallelogram properties to answer our given problems.

(1) Since we know that opposite sides of parallelogram are congruent, therefore measure of side MN and side KN will be equal to the measure of their opposite sides.

LM=KN and KL=MN

Upon substituting our given values we will get,

45=KN and 31=MN

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

We have been given $m\angle N=119^{o}$ , therefore $m\angle L=119^{o}$ .

We will find measure of angle K by using supplementary angles.

$m\angle N+m\angle M=180^{o}$

$119^{o}+m\angle M=180^{o}$

$m\angle M=(180-119)^{o}$

$m\angle M=61^{o}$

By opposite angles of parallelogram $m\angle K=61^{o}$ .

(2) Opposite sides of parallelogram are equal. Therefore, CF=DE and FE=CD.

Upon substituting our given values we will get,

CF=10 and FE=15.

Property: Diagonals of parallelogram bisect each other.

So CE will be 2 times CG and GD will be half the length of FD.

$CE=2\times 7=14$

$GD=\frac{1}{2}\times 22=11$

(3) Property: Opposite sides of parallelogram are congruent.

$SR=PQ$ and $QR=PS$

Upon substituting our given values we will get,

$SR=24$ and $QR=19$

Property: Diagonals of parallelogram bisect each other.

So SQ will be 2 times TQ and PT will be half the length of PR.

$SQ=2\times 10=20$

$PT=\frac{1}{2}\times 42=21$

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

$m\angle PQR=106^{o}$

$m\angle PQS=m\angle QSR$ Alternate interior angles.

$m\angle PQS=49^{o}$

$m\angle QRS=m\angle QPS$ Opposite angles of parallelogram.

$m\angle PQR+m\angle QPS=180^{o}$

$106^{o}+m\angle QPS=180^{o}$

$m\angle QPS=180^{o}-106^{o}$

$m\angle QPS=74^{o}$

Therefore, measure of angle QRS will 74 degrees.

$m\angle PRS=m\angle QPR$ Alternate interior angles.

$35^{o}=m\angle QPR$

$m\angle RPS=74^{o}-m\angle QPR$

$m\angle RPS=74^{o}-35^{o}$

$m\angle RPS=39^{o}$

Now let us find measure of angle PSQ.

$m\angle PSQ=m\angle PQR-m\angle QSR$

$m\angle PSQ=106^{o}-49^{o}$

$m\angle PSQ=57^{o}$

The image is not clear, so I am unable to answer the last two problems.

5 0

3 years ago

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The coordinates below represent two linear equations. How many solutions does this system of equations have?

d1i1m1o1n [39]

Use the points to find the equations of both your lines.
By using the formula for finding slope where: m = (y2-y1) / (x2-x1)
Your first equation is y = -2x+4
Your second equation is y = -2x+7
Normally you want to set these equal to each other and see where they are equal... however, as you can clearly see, these two equations are parallel. Parallel equations don't intersect, which would mean your answer is A, no solutions.

3 0

3 years ago

What is 6x8+90-4 thank you

faust18 [17]

178 is the anwser thank you

4 0

4 years ago

Find the next two terms in the sequence 1/3, 1/9,1/27,1/81....

netineya [11]

1/243

each second number is being multiplied by three

3*3=9

9*3=27

27*3=81

so 81*3=243

243 is the answer

3 0

3 years ago

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