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LekaFEV [45]
1 year ago
15

A box has twice as many grapes as a basket. Once 2kg of grapes were added to the basket, it contained 0.5 kg more than the box.

How many kilograms of grapes are in the basket now?
Mathematics
1 answer:
pav-90 [236]1 year ago
3 0

By solving a system of equations, we will see that now there are 3.5kg of grapes on the basket.

<h3>How many kilograms of grapes are in the basket now?</h3>

Let's define the variables:

  • x = kg of grapes on the box originally.
  • y = kg of grapes on the basket originally.

We know that:

x = 2y

When we add 2kg to the basket, it has 0.5k more than the box, then:

y + 2 = x + 0.5

Then we have a system of equations:

x = 2y

y + 2 = x + 0.5

We want to solve this for y, then we can replace the first equation into the second one:

y + 2 = (x = 2y) + 0.5

y + 2 = 2y + 0.5

2 - 0.5 = 2y - y

1.5 = y

This means that, originally, there are 1.5 kg of grapes on the basket. And then we added 2kg, so now there are:

1.5kg + 2kg = 3.5kg

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

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Find the coordinates of the point 7/10 of the way from A to B. a=(-3,-6) b=(12,4)
Artemon [7]

Answer:

The coordinates of M are x = \frac{15}{2} and y = 1.

Step-by-step explanation:

Let be A = (-3,-6) and B = (12, 4) endpoints of segment AB and M a point located 7/10 the way from A to B. Vectorially, we get this formula:

\overrightarrow {AM} = \frac{7}{10}\cdot \overrightarrow {AB}

\vec M - \vec A = \frac{7}{10}\cdot (\vec B - \vec A)

By Linear Algebra we get the location of M:

\vec M = \vec A + \frac{7}{10}\cdot (\vec B - \vec A)

\vec M = \vec A +\frac{7}{10}\cdot \vec B - \frac{7}{10}\cdot \vec A

\vec M = \frac{3}{10}\cdot \vec A + \frac{7}{10}\cdot  \vec B

If we know that \vec A = (-3,-6) and \vec B = (12, 4), then:

\vec M = \frac{3}{10}\cdot (-3,-6)+\frac{7}{10}\cdot (12,4)

\vec M = \left(-\frac{9}{10},-\frac{9}{5}  \right)+\left(\frac{42}{5} ,\frac{14}{5} \right)

\vec M =\left(-\frac{9}{10}+\frac{42}{5} ,-\frac{9}{5}+\frac{14}{5}   \right)

\vec M = \left(\frac{15}{2} ,1\right)

The coordinates of M are x = \frac{15}{2} and y = 1.

6 0
3 years ago
How to find the height of a tree in cm. 5m and 4m equal how many cm
erastova [34]
The answer is 9 cm 

Hope that helps! :)
3 0
3 years ago
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Please find the answer to this function! F(2)= 6x^4-10x^3+40x-50
steposvetlana [31]

<u>Answer-</u>

f(2)= 6x^4-10x^3+40x-50=46

<u>Solution-</u>

The given function is,

\Rightarrow f(x)= 6x^4-10x^3+40x-50

Now, we have to find the value of f(x) at x=2 i.e f(2), so putting x as 2 in the given function,

\Rightarrow f(2)= 6(2)^4-10(2)^3+40(2)-50

\Rightarrow f(2)= (6\times 16)-(10\times 8)+(40\times 2)-50

\Rightarrow f(2)= (6\times 16)-(10\times 8)+(40\times 2)-50

\Rightarrow f(2)= 96-80+80-50

\Rightarrow f(2)= 96-50

\Rightarrow f(2)= 46

Therefore, f(2) was found to be 46.


7 0
3 years ago
Write the equation of the line that passes through the given points (-6, 0) and (0, 3)
Tomtit [17]

Answer:

Step-by-step explanation:

Put (-6,0) and (0,3) into a table of values

form of the equation: mx+b

x -6 0

y 0 3

3/-6=-0.5 (m)

3=b (the value of y when x=0)

equation: y=0.5x+3

3 0
3 years ago
1. Write a two-column proof for the following conjecture. You may not need to use all of the rows of the two-column table provid
marshall27 [118]

Answer:  

Given: ABCD is a parallelogram.

Prove: Angle A and B are supplementary and C and D are supplementary.

That is, m∠A + m∠B = 180° and m∠C + m∠D = 180°


                Statement                                                Reason

1. ABCD is a parallelogram              1. Given  

2.m∠A=m∠C and m∠B=m∠D         2. Definition of parallelogram.

3.m∠A+m∠B+m∠C+m∠D=360°      3. Definition of quadrilateral

4. m∠A+m∠B+m∠A+m∠B=360°     4. By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

Similarly, m∠C + m∠D = 180°

5.∠A and ∠C are supplementary,  5. Def. of Supplementary

∠ B and ∠D are supplementary

7 0
3 years ago
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