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aivan3 [116]
3 years ago
15

Daniel can by a particular brand of juice in a 6 ounce bottle or a 10 ounce bottle the juice in a 10 ounce bottle contains 150 c

al calories how many calories are in a 6 ounce bottle
Mathematics
1 answer:
olasank [31]3 years ago
7 0

Answer: There are 90 calories in a 6-ounce bottle.

Step-by-step explanation:

We assume that the quantity of juice in the bottle is directly proportional to the number of calories it contains.

Given: 10 ounces of juice has 150 calories.

i.e. 1 ounce of juice has \dfrac{150}{10} calories.

i.e. 1 ounce of juice has 15 calories.

Now, In 6 ounce of juice, the number if calories = 15 x 6 = 90 calories

Hence, there are 90 calories in a 6-ounce bottle.

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Write the equation of the function whose graph is shown. y = (x + )2 +
Deffense [45]
Quadratic form is given in the form
y= ax^{2}+bx+c, where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

12= a(8)^{2}+b(8)+c
12=64a+8b+c ... Equation 1

3=a(5)^{2}+b(5)+c
3=25a+5b+c ... Equation 2

Equation 1 - Equation 2 gives
39a+3b=9, we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of x is given by x=- \frac{b}{2a}
Substitute x=5
5=- \frac{b}{2a}
10a=-b
b=-10a ... Equation 4

Substitute Equation 4 into Equation 3
39a+3b=9
39a+3(-10a)=9
39a-30a=9
9a=9
a=1

Now we need to work out the value of b and c

Substitute a=1 back into equation 4
-10a=b
-10(1)=b
b=-10

Substitute a=1 and b=-10 into either equation 1 or equation 2

64a+8b+c=12
64(1)+8(-10)+c=12
64-80+c=12
c=12+80-64
c=28

Hence the equation of the quadratic curve is
y= x^{2} 10x+28


8 0
3 years ago
Read 2 more answers
Department started out with 100 pencils and 200 pens during the lat quarter of this year they lost 4% of the pens and 2% of the
o-na [289]

Answer:

The remaining number of the pencil   =  98

The remaining number of the pens  =  192

Step-by-step explanation:

Here, according to the question:

The number of pencils at the starting at the quarter = 100

The percentage of the lost pencil over the year = 2%

Now, calculating the lost pencil, we get:

2% of 100 = \frac{2}{100}  \times 100 = 2

⇒The number of lost pencil over the year = 2

So,Number of remaining Pencil = Total pencil - Number of pencil lost

                                                       = 100 - 2 = 98

The number of pens at the starting at the quarter = 200

The percentage of the lost pens over the year = 4%

Now, calculating the lost pens, we get:

4% of 200 = \frac{4}{100}  \times 200 = 8

⇒The number of lost pens over the year = 8

So,Number of remaining Pens = Total pens - Number of pens lost

                                                       = 200 - 8 = 192

Hence, the remaining number of the pencil   =  98

And and the remaining number of the pens at the end of the year  = 192

6 0
3 years ago
Which equation represents direct variation, if k represents the constant of variation? A) y = kx B) yx = k C) y = kx2 D) y = kxz
Leto [7]
Y = kx

the question ask for "direct vation"...the formula must always to be y at the left side and k at the right side
5 0
3 years ago
Read 2 more answers
How do you solve for x <br><br>the similarity statement is abc~ xyz​
tensa zangetsu [6.8K]

Answer:

m<X= 36.87 degrees

Step-by-step explanation:

Since the triangle abc and xyz are similar, hence;

m<C = m<Y

90 = x - 5

Add 5 to both sides

90+5 = x-5+5

95 = x

Swap

x = 95

m<Y = x - 5

m<Y = 95 - 5

m<Y = 90

Find m<X

Using the SOH CAH TOA

Opposite to m<X = YZ = 6

Adjacent = 8

Tan M<X = opp/adj

Tan m<X = 6/8

m<X = arctan(6/8)

m<X= 36.87 degrees

8 0
3 years ago
If 30% of a number, p, is 240, what is 72% of p? giving brainliest
Mnenie [13.5K]

Answer:

576

Step-by-step explanation:

30/ 100 x p = 240

p = 240 x 100/30 = 800

72/ 100 x p=

72/100 x 800 = 576

I hope im right!!

3 0
3 years ago
Read 2 more answers
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