(b) What does the shaded region represents in the given figure?

Subject : Maths Level : High school Topic : Surds Points : 72

Mila [183]

Answer:

a = 5

Step-by-step explanation:

Simplify:

√5(√8 + √18) =
√5*8 + √5*18 =
√40 + √90 =
√4*10 + √9*10 =
2√10 + 3√10 =
(2 + 3)√10 =
5√10

The value of a:

a√10 = 5√10
a = 5

6 0

3 years ago

Tyler went to the super market to buy food for a pantry. He has $36, and can carry up to 20pounds of food in his backpack. One p

AleksAgata [21]

This question is incomplete

Complete Question

Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? Explain your reasoning.

Answer:

Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.

Step-by-step explanation:

Let

x = the number of packages of pasta

y = the number of jars of pasta sauce.

He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.

x + 1.5y ≤ 20....... Equation 1

x = 20 - 1.5y

x × $1 + y × $3 = $36

x + 3y ≤ 36..... Equation 2

20 - 1.5y + 3y = 36

-1.5y + 3y = 36 - 20

1.5y = 16

y = 16/1.5

y = 8

And x = 8

Therefore,

Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.

6 0

2 years ago

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock.

ddd [48]

The answer is 4 3/4 yards of the fabric.

This can be calculated using the proportion.
If the 3 1/6 yards of the fabric is enough for 1 1/3 shirts, how many yards are necessary of 2 shirts:
 $3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts$

Let's express 3 1/6 as 19/6:
$3 \frac{1}{6} =3+ \frac{1}{6} = 3* \frac{6}{6}+ \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{18+1}{6} = \frac{19}{6}$

Similarly, 1 1/3 = 4/3:
$1 \frac{1}{3} =1+ \frac{1}{3} = 1* \frac{3}{3}+ \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{3+1}{3} = \frac{4}{3}$

Now, let's use this in the proportion:
 $3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts$
 $\frac{19}{6} : \frac{4}{3} = x:2$

Crossing the products:
$x* \frac{4}{3} =2* \frac{19}{6}$
⇒ $x* \frac{4}{3} = \frac{19}{3}$
⇒ $x = \frac{19}{3} : \frac{4}{3}$
$x= \frac{19}{3} * \frac{3}{4}$
⇒ $x = \frac{19}{4} = \frac{16+3}{4} = \frac{16}{4} + \frac{3}{4} =4+ \frac{3}{4} =4 \frac{3}{4}$

Therefore, Mary needs in total 4 3/4 yards of the fabric.

6 0

2 years ago

Read 2 more answers

-(-5 - 6x) = 4 (5x +3)

tatiyna

-(-5 - 6x) = 4 (5x +3)

Pretend that there is a -1 in front of the first bracket

-1(-5-6x)= 4(5x+3)

Mutiply the first bracket by -1

(-1)(-5)(-1)(-6x)= 5+6x

Mutiply the second bracket by 4

(4)(5x)(4)(3)= 20x+12

5+6x= 20x+12

move 20x to the other side

5+6x-20x= 20x-20x+12

5+6x-20x= 12

5-14x= 12

move 5 to the other side

sign changes from +5 to -5.

5-5-14x= 12-5

-14x=7

divide by -14

-14x/-14= 7/-14

x= -1/2

Answer: x= -1/2

6 0

3 years ago

Joe's canoe charges an initial fee of $20 plus $4 an hour. Callie's canoe charges a flat rate of $14 an hour find the number of

irinina [24]

Initial fee charged by Joe's canoe = $20
Hourly charge of Joe's canoe = $4
Hourly charge of Callie's canoe = $14
No initial fee is taken by Callie's canoe.
Let us assume the number of hours after which both places charges will be the same = x hours
Then
20 + 4x = 14x
20 = 14x - 4x
20 = 10x
x = 20/10
= 2
So after 2 hours the charges taken by both of them will be the same. I hope the procedure is easy and clear enough for you to understand.

3 0

2 years ago

Read 2 more answers

(b) What does the shaded region represents in the given figure?​

(b) What does the shaded region represents in the given figure?