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3 years ago

The diagram above shows a circle with centre O and radius 25 cm.

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Answer:

Step-by-step explanation:

Notice that KL = LM and PQ = QR since OL and OQ are perpendicular to both KM and PR.

It follows that QR = (1/2) PR = 20 cm. We also know that MR = 21.

Now in order to solve the problem we just need OQ=OL

$OQ^2=OR^2-QR^2= 25^2-20^2 =225\\OQ=15$

Therefore the perimeter of the pentagon is

$OL+LM+MR+RQ+Q)\\= 15+20+21+20+15= 91$

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Which expressions are equivalent to 2(4f+2g)?

zzz [600]

Answers are C) 8f+4g D) 4(2f+g) & E) 4f+4f+4g

4 0

3 years ago

A chemist wants to mix a solution of 20% chlorine with a solution of 60% chlorine to make 120 liters of 30% solution of chlorine

Mama L [17]

Answer:

90 and 30 liters

Step-by-step explanation:

1) if solution of 20% is 'x' and of 60% is 'y' liters, then

2) the pure chlorine is: for solution of 20% - 0.2x, for solution of 60% - 0.6y and

3) the mix of the two solutions is 120=x+y.

4) using these items it is possible to make up the system of two equations:

$\left \{ {{x+y=120} \atop {0.2x+0.6y=0.3(x+y)}} \right.$

5) finally, x=90 liters of 20%; y=30 liters of 60% solution.

8 0

3 years ago

Find a quadratic function that includes the set of values below. (0,9). (2,15) (3,12)

nlexa [21]

Answer:

$f(x) = -2x^2 + 7x + 9$

Step-by-step explanation:

$f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9$

3 0

4 years ago

Callie has a new kitten. They can weigh 3 pounds less than half the weight of Callie‘s cat. Together the cat and kitten weigh 18

gavmur [86]

Answer:

The weight of cat is 14 pounds and the weight of kitten is 4 pounds.

Step-by-step explanation:

Given:

Callie has a new kitten. It can weigh 3 pounds less than half the weight of Callie‘s cat. Together the cat and kitten weigh 18 pounds.

Now, to find the weight of each animal:

Let the cat's weight be $x.$

And the kitten weight = $\frac{x}{2} -3$

Total weight of cat and kitten = 18 pounds.

Now, to set an equation to get the weight of each animal:

$(x)+(\frac{x}{2}-3)=18$

$x+\frac{x}{2} -3=18$

$\frac{2x+x-6}{2} =18$

$\frac{3x-6}{2} =18$

Multiplying both sides by 2 we get:

$3x-6=36$

Adding both sides by 6 we get:

$3x=42$

Dividing both sides by 3 we get:

$x=14\ pounds.$

The weight of cat = 14 pounds.

Substituting the value of $x$ to get the kitten's weight:

$\frac{x}{2} -3\\\\=\frac{14}{2}-3\\\\=7-3\\\\=4.$

The kitten's weight = 4 pounds.

Therefore, the weight of cat is 14 pounds and the weight of kitten is 4 pounds.

7 0

3 years ago

A laundry bag contains 7 brown socks and 2 black socks. Find the probability of picking a brown sock first,

PilotLPTM [1.2K]

Answer

7/9 chance to pick a brown sock first and 1/4 chance to get a black sock after

Step-by-step explanation:

there are 9 total socks and 7 are brown so you will have a 7/9 chance to get a brown sock

then if you do get a brown the total number of socks will be 8 in the bag so then you have a 2/8 chance which can be simplified to 1/4

6 0

4 years ago