Mathematics, 01.10.2019 10:30 wolfgirl10000

Addison paid $10 for 2 granola bars and 6 apples. george paid $7 for 2 granola bars and 3 apples. find the cost of each granola bar and each apple.

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Answer from: ultimatesaiyan

g(granola bar) = $2 and a(apple) = $1

Step-by-step explanation:

This problem can be modeling as an equation systems with two unknows.

We can writting the equation systems as follows:

For Addison 2g+6a=10 where "g" is a granola bar price, "a" an apple price, and 10 is the sum of both product prices in dollars.

For George 2g+3a=7 where "g" is a granola bar price, "a" an apple price, and 7 is the sum of both product prices in dollars.

Ordering both equations:

$\left \{ {{2g+6a=10} \atop {2g+3a=7}} \right.$

We're going to use the reduction method to solve this system of equations.

The reduction method consists of adding (or subtracting) the system equations to eliminate one of the unknowns.

1. Make sure that adding or subtracting the equations, some of the unknowns disappears.

We can see if we substracting both equations, the "g" unknown disappears.

$\left \{ {{2g+6a=10} \atop {-(2g+3a)=-(7)}} \right.$

$\left \{ {{2g+6a=10} \atop {-2g-3a=-7}} \right.$

Sustracting both equations, we obtain:

0g+3a=3

3a=3

$a=\frac{3}{3} =1$ which means that the value of an apple is $1.

2. We calculate the other unknown by substituting the value obtained from "a".

Substituting the value from "a" in the first equation:

2g+6(1)=10

2g+6=10

2g=10-6

$g=\frac{10-6}{2}$

$g=\frac{4}{2}$

g=2 which means that the value of a granola bar is $2.

3. Finally, we verify the result by substituting the values obtained for "g" and "a" to see if it satisfy the equations.

For the first equation:

2g+6a=10 with g = 2 and a = 1

2(2)+6(1)=10

4+6=10

For the second equation:

2g+3a=7 with g = 2 and a = 1

2(2)+3(1)=7

4+3=7

Answer from: Quest

about 5.6 days

step-by-step explanation:

we can fill the given information into the decay equation and solve for the value of t at which half the sample remains.

$\dfrac{11}{2} =11e^{-0.1247t} \qquad\text{decay equation with values filled in}\\\\\dfrac{1}{2}=e^{-0.1247t} \qquad\text{divide by 11}\\\\-\ln{(2)}=-0.1247t \qquad\text{take the natural log}\\\\\dfrac{\ln{(2)}}{0.1247}=t\approx 5.559\approx 5.6\qquad\text{divide by -0.1247}$

the half-life is about 5.6 days.

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Addison paid $10 for 2 granola bars and 6 apples. george paid $7 for 2 granola bars and 3 apples. fi...

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