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anygoal [31]
3 years ago
14

Using the following diagram, solve for x.

Mathematics
2 answers:
yuradex [85]3 years ago
6 0
The answer to this equation is x=63
storchak [24]3 years ago
4 0

Answer:

x=10.5

Step-by-step explanation:

Use Thales' Theorem which says: If two lines, not necessarily parallel, are cut by a system of parallel lines, then the segments that result on one of the two lines are proportional to the corresponding segments obtained on the other.

Take a look at the picture I attached you, from it, It is true that:

\frac{AB}{A'B'} =\frac{BC}{B'C'}

Hence:

\frac{12}{6} =\frac{21}{x}

Solving for x:

x=\frac{21}{2} =10.5

You might be interested in
How many axes of symmetry has a rhombus
Kitty [74]
Rhombus has 2 axes of symetry (they contain diagonals).

If rhombus is a square then has 4 axes of symetry.

3 0
3 years ago
Ella has 0.5 lb of sugar. how much water should she add to make the following concentrations? Tell Ella how much syrup she will
makkiz [27]

Answer:

For 50% syrup, add 0.5 lb of water for 1 lb of syrup; for 5% syrup, add 9.5 lb of water for 10 lb of syrup; for 75% syrup, add 0.17 lb of water for 0.67 lb of syrup; for 1.5% syrup, add 32.8 lb of water for 33.3 lb of syrup.

Step-by-step explanation:

Let x represent the amount of water added.  This means the total mass of the syrup is represented by 0.5+x.

To find percentages, we divide the part by the whole.  For a 50% syrup, we need the part (sugar) compared to the whole (sugar + water) to equal 50%, or 0.50:

Multiply both sides by 0.5+x:

Using the distributive property, we have

0.5 = 0.5(0.5)+0.5(x)

0.5 = 0.25+0.5x

Subtract 0.25 from each side:

0.5-0.25 = 0.25+0.5x-0.25

0.25 = 0.5x

Divide both sides by 0.5:

0.25/0.5 = 0.5x/0.5

x = 0.5

For 50% syrup, add 0.5 lb of water.  This makes the total mass 0.5+0.5 = 1 lb.

For 5% syrup, we change the equation to equal 0.05 (5% = 5/100 = 0.05) and leave everything else the same:

Multiply both sides by 0.5+x:

Using the distributive property,

0.5 = 0.05(0.5)+0.05(x)

0.5 = 0.025 + 0.05x

Subtract 0.025 from both sides:

0.5-0.025 = 0.025+0.05x-0.025

0.475 = 0.05x

Divide both sides by 0.05:

0.475/0.05 = 0.05x/0.05

x = 9.5

For 5% syrup, add 9.5 lb of water; the total mass will be 9.5+0.5 = 10 lb.

For 75% syrup, set the equation equal to 0.75:

Using the distributive property,

0.5 = 0.75(0.5)+0.75(x)

0.5 = 0.375 + 0.75x

Subtract 0.375 from each side:

0.5 - 0.375 = 0.375 + 0.75x - 0.375

0.125 = 0.75x

Divide both sides by 0.75:

0.125/0.75 = 0.75x/0.75

0.17 = x

For 75% syrup, add 0.17 lb of water; the total mass is 0.17+0.5 = 0.67 lb.

For 1.5% syrup, set the equation equal to 0.015:

Using the distributive property,

0.5 = 0.015(0.5) + 0.015(x)

0.5 = 0.0075 + 0.015x

Subtract 0.0075 from each side:

0.5-0.0075 = 0.0075 + 0.015x - 0.0075

0.4925 = 0.015x

Divide both sides by 0.015:

0.4925/0.015 = 0.015x/0.015

32.8 = x

For 1.5% syrup, use 32.8 lb of water; the total mass is 32.8+0.5 = 33.3 lb.

I hope this is right and have a good day

3 0
2 years ago
Read 2 more answers
Find the volume of a pyramid with a square base, where the perimeter of the base is
Yuki888 [10]

Answer:

V= 57.8 cm^3

Step-by-step explanation:

i had the same question and got it wrong and it showed me the correct answer so basically

V=1/3(11.56(15)

V=57.8

3 0
3 years ago
Martina jarred 9 liters of jam after 3 days. How much jam did Martina jar if she spent 6 days making jam? Assume the relationshi
alina1380 [7]

Answer:

18

Step-by-step explanation:

since there are 9 liters and three days, you double the amount of days to get 6, so you do the same to the amount of liter she makes. so 18 liters of jam

5 0
3 years ago
Helpppppp I forgot
ivann1987 [24]
30 
multiply 3.0 times 10 
3 0
3 years ago
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