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Vlad [161]
2 years ago
9

Please help with these two questions worth 35 points: Question 1: 6 people equally share 56 gummy worms. How many gummy worms do

es each person get?
A nine and one sixth gummy worms
B nine and two sixths gummy worms
C ten and one sixth gummy worms
D ten and two eighths gummy worms

Question 2: Carrie makes 27 liters of lemonade. 8 people share the lemonade equally. Which statement is true?

A Each person will receive less than 2 liters.
b Each person will receive between 2 and 3 liters.
c Each person will receive between 3 and 4 liters.
d Each person will receive more than 4 liters.
Mathematics
1 answer:
ASHA 777 [7]2 years ago
3 0
Question 1: B- 9 2/6

Question 2: C btw 3-4 liters each
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For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog
natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ  ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}

\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

∠GAB = 22.62°

cos(\angle GAB) =  \dfrac{36}{39} = \dfrac{12}{GH}

GH =  \dfrac{39}{36} \times {12}

GH = 13 in.

∴ AD 13 in.

BP = 39 × sin(22.62°) = 15 in.

GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²

7 0
3 years ago
Read 2 more answers
Hàm số nào là hàm lẻ<br> A sin^2 x+1 B cot^3x C tn3x cotx d cosx
Sedaia [141]
{(sin (x))^2A(csc(x))^3(cos))3B+(-3x)
{cot (dx) cos (x)
6 0
2 years ago
If y= 1/2x and x= -14, find y
malfutka [58]

Answer:

y=-1/28

Step-by-step explanation:

y=1/2(-14)

y=1/-28

8 0
3 years ago
A father’s age now is three times the age that his son was 4 years ago. In
Mice21 [21]
Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.

4 years ago, the son was:

s-4

So, his father is currently:

3(s-4)

=

3s-12

Therefore:

f = 3s-12

In twelve years, the son will be:

s+12

And the father will be:

f+12

This can also be written as:

3s-12+12 as the fathers younger age would be f = 3s+12

=

3s

So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36

Son’s current age: 36

We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.

2(24)+24 = 72

Father’s current age: 72










7 0
1 year ago
A box without a top is made from a rectangular piece of cardboard, with dimensions 27 centimeters by 18 centimeters, by cutting
GaryK [48]
By cutting each corner we have that the resulting dimensions are:
 27 - 2x
 18 - 2x
 Height = x
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 V (x) = (x) * (27-2x) * (18-2x)
 Answer:
 
The volume of the box in terms of x is:
 
(27-x) (18-x) x
8 0
3 years ago
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