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3 years ago

A number is doubled and then increased by nine. The result is ninety- Three. What is the original number?

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

First you subtract 93 by 9. You get 84. Then you divide it by 2. Which is your answer, 42.

This can be represented as:

93=2x+9

First subtract 9 from both sides

84=2x

Then divide by 2 on both sides

42=x

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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

2 years ago

What are the solutions to the quadratic equation <img src="https://tex.z-dn.net/?f=x%5E2%20%2B40%3D0" id="TexFormula1" title="x^

Mandarinka [93]

Answer:

In disguise right arrow In Standard Form a, b and c

x2 = 3x − 1 Move all terms to left hand side x2 − 3x + 1 = 0 a=1, b=−3, c=1

2(w2 − 2w) = 5 Expand (undo the brackets),

and move 5 to left 2w2 − 4w − 5 = 0 a=2, b=−4, c=−5

z(z−1) = 3 Expand, and move 3 to left z2 − z − 3 = 0 a=1, b=−1, c=−3

Step-by-step explanation:

sorry it took so long

7 0

3 years ago

Is the product 1.01 1.01 less than or greater than 1?

faust18 [17]

Answer:

greater than 1

Step-by-step explanation:

its greater because 1.01 is greater than 1

8 0

3 years ago

How can you use a point on the graph of f –1(x) = 9x to determine a point on the graph of f(x) = log9x?

Anastasy [175]

Whenever you can invert a function, you have that the graphs of $f(x)$ and its inverse $f^{-1}(x)$ are reflected with respect to the line $y=x$

So, given any point on the graph of $f^{-1}(x)$ , you can simply swap its coordinates to get the correspondent point on the original function $f(x)$

As an example, all exponential functions pass through the point $(0,1)$ , while all the logarithmic functions pass through the point $(1,0)$

6 0

3 years ago

Read 2 more answers

Jacob opened a money-market account. In the first month, he made an initial deposit of $500, and

natima [27]

Answer:

after 13 months

Step-by-step explanation:

........ur welcome..........

1475-500=975

975÷75=13

so 13 months

6 0

3 years ago