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2 years ago

Why are decimals called decimals?

Mathematics

1 answer:

natta225 [31]2 years ago

8 0

Answer:

Step-by-step explanation:

Decimal comes from the Latin word decimus, meaning tenth, from the root word decem, or 10. The decimal system, therefore, has 10 as its base and is sometimes called a base-10 system. Decimal can also specifically refer to a number in the decimal system.

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How many solutions does the system of equations below have?

soldier1979 [14.2K]

Answer:

One solution

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

$\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}$

$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

$y = - \dfrac{ 5 }{ 6 }$

$\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}$

So there is only one solution to the equation.

5 0

1 year ago

Question #10 Evaluate the expression: 18-3(1+4)

Mashutka [201]

Answer:

18-3-12

15-12

3 is the answer

hope this helps

have a good day :)

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Find the approximate solution of this system of equations. y=x^2+5x+3 y=square root2x+5

Anni [7]

We have that
y=x²<span>+5x+3
y=</span>√(<span>2x+5)

using a graph tool
see the attached figure

the solution is
x=-0.175
y=2.156

therefore

the answer is the option
</span>B.) (-0.2, 2.1)

6 0

2 years ago

Read 2 more answers

Jenny thinks that the expression below is equal to x²-4. If you agree, show that she is correct. If you disagree, show that she

sergiy2304 [10]

Answer:

Jenny is wrong the correct answer is x²+ 4 - 4 x.

Step-by-step explanation:

Given that

(x-2)³∕x-2

(x-2)³∕(x-2) =(x-2) (x-2)²∕(x-2)

(x-2)³∕(x-2) = (x-2)²

As we know that

(a-b)² = a²+b² - 2 ab

(x-2)² = x²+ 2² - 2 ˣ 2 ˣ x = x²+ 4 - 4 x

(x-2)² = x²+ 4 - 4 x

It means that

(x-2)³∕(x-2) = (x-2)² = x²+ 4 - 4 x

So Jenny is wrong the correct answer is x²+ 4 - 4 x.

8 0

2 years ago

What are the measures of the missing angles x°, y° of a regular triangle if one angle measure equals 60°?

MArishka [77]

Answer:

So each interior angle measurement of the regular triangle is 60 degrees.

Step-by-step explanation:

If the triangle is regular, this means all the side measurements are congruent to each other and that all the angle measurements are congruent to each other.

If the sum of the angles in a triangle is 180 degrees and you know they are each the same then you could either solve x+x+x=180 or know we are just dealings with an equiangular triangle in which all angles have measurement 60 degrees.

If need more convincing, let's actually solve:

x+x+x=180

3x=180

x=180/3

x=60

So each interior angle measurement of the regular triangle is 60 degrees.

3 0

2 years ago

Why are decimals called decimals? ​

Why are decimals called decimals?