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2 years ago

Solve the expression 2(10)+2(x-4) show your work

Mathematics

1 answer:

Nataliya [291]2 years ago

4 0

Answer:

12 + 2x

Step-by-step explanation:

simplifying expression:

2(10) + 2(x-4)

2 × 10 = 20

2 × x = 2x

2 × -4 = -8

20 + 2x - 8

20 - 8 = 12

12 + 2x

if you want to simplify it more:

(12/2) + (2x/2)

2(6 + x)

if you want to solve for x:

12 + 2x = 0

(12 - 12) + 2x = (0 - 12)

2x/2 = -12/2

x = -6

hope this helps you!

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All the info is in the pictures

Hunter-Best [27]

Bearing in mind that an absolute value expression is in effect a piece-wise function with two cases, thus

$\bf |-n|=
\begin{cases}
+(-n)\\
-(-n)
\end{cases}\implies 
\begin{cases}
-n\\
n
\end{cases}
\\\\\\
n|-n|=2n\implies 
\begin{cases}
n-n=2n\implies 0=2n\implies &0=n\\
n+n=2n\implies 2n=2n\impliedby &inconsistent
\end{cases}$

6 0

3 years ago

What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?

Brut [27]

The length of the shorter leg is 14 inches.

We will set up two equations for this; first, for the perimeter. We will call the legs a and b:

a + b + 50 = 112

Subtract 50 from both sides:
a + b + 50 - 50 = 112 - 50
a + b = 62

We will isolate a, so we can use substitution. Subtract b from both sides:
a + b - b = 62 - b
a = 62 - b

Now we will set up our Pythagorean theorem equation:
a² + b² = 50²
a² + b² = 2500

We will substitute our value for a from the first equation into this one:
(62-b)² + b² = 2500
(62 - b)(62 - b) + b² = 2500

Multiplying the binomials, we have:
62*62 - b*62 - b*62 -b(-b) + b² = 2500
3844 - 62b - 62b + b² + b² = 2500

Combining like terms:
3844 - 124b + 2b² = 2500

To set it equal to 0 and solve, we subtract 2500 from both sides:
3844 - 124b + 2b² - 2500 = 2500 - 2500
1344 - 124b + 2b² = 0

In standard form, we have
2b² - 124b + 1344 = 0

Using the quadratic formula,
$\frac{--124\pm \sqrt{(-124)^2-4(2)(1344)}}{2(2)}
\\
\\=\frac{124\pm \sqrt{15376-10752}}{4}
\\
\\=\frac{124\pm \sqrt{4624}}{4}=\frac{124\pm 68}{4}=\frac{124+68}{4}\text{ or }\frac{124-68}{4}
\\
\\=\frac{192}{4}\text{ or }\frac{56}{4}=48\text{ or }14$

The shorter leg is 14 and the longer one is 48.

8 0

3 years ago

Read 2 more answers

Match solutions and differential equations. Note: Each equation may have more than one solution. Select all that apply. (a) 7y''

Nonamiya [84]

Answer:

a- $e^x,e^{-x}$

b- $x^{-2}$

c- $x^3$

Step-by-step explanation:

a.7 y''-7 y =0

Auxillary equation

$D^2-1=0$

$(D-1)(D+1)=0$

D=1,-1

Then , the solution of given differential equation

$y=e^x,y=e^{-x}$

2. $7x^2y''+14xy'-14 y=0$

Y= $y=x^3$

$y=3x^2$

$y''=6x$

Substitute in the given differential equation

$42x^3+42x^3-14x^3\neq 0$

Hence, $x^3$ is not a solution of given differential equation

$e^x,e^{-x}$ are also not a solution of given differential equation.

y= $x^{-2}$

$y'=-2x^{-3}$

$y''=6x^{-4}$

Substitute the values in the differential equation

$7x^2(6x^{-4})+14x(-2x^{-3})-14 x^{-2}$

= $42x^{-2}-28x^{-2}-14x^{-2}=0$

Hence, $x^{-2}$ is a solution of given differential equation.

c. $7x^2y''-42y=0$

$y=x^3$

$y'=3x^2$

$y''=6x$

Substitute the values in the differential equation

$42x^3-42x^3=0$

Hence, $x^3$ is a solution of given differential equation.

a- $e^x,e^{-x}$

b- $x^{-2}$

c- $x^3$

6 0

3 years ago

Read 2 more answers

g A test was conducted to determine if there is a difference between Canadian and American average heart rates. A group of 36 Ca

melisa1 [442]

Answer:

The test statistic | t | =4.45

Step-by-step explanation:

Step(i):-

Given that the first sample size n₁ = 36

Given that the second sample size n₂ = 34

Mean of the first sample x₁⁻ = 68.5

Mean of the second sample x₂⁻ = 70

Step(ii):-

Test statistic

$t = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } } )}$

$t = \frac{68.5-70}{\sqrt{2(\frac{1}{36}+\frac{1}{34} ) } }$

$t = \frac{-1.5}{0.337} = -4.45$

The test statistic | t | = |-4.45| =4.45

6 0

2 years ago

Answer to the question

natta225 [31]

Answer:

Value of x = -1 and y = -4

Step-by-step explanation:

BC = 3 (given)

BC = AD ( opposite sides of a parallelogram are equal)

∴ AD = 3

AD = x - y (given)

∴ 3 = x - y

3 + y = x -------- (1)

CD = 2 (given)

CD = AB (opposite sides of a parallelogram are equal)

∴ AB = 2

AB = 2x - y (given)

∴ 2 = 2x - y ----------- (2)

Putting the value of x in (1) To (2)

2 = 2(3+y) - y

2 = 6 + 2y - y

2 = 6 + y

2 - 6 = y

-4 = y

Now, substitute the value of y in (1)

x = 3 + y

x = 3 + (-4)

x = 3 - 4

x = -1

Therefore, the value of x = -1 and y = -4.

Cross-checking

2x - y = 2

2*-1 - (-4) = 2

-2 -(-4) = 2

-2 + 4 = 2

2 = 2

LHS = RHS

x - y = 3

-1 -(-4) = 3

-1+4 = 3

3 = 3

LHS = RHS

Thus verified

Hope u understand

Please mark as brainliest

Thank You

6 0

3 years ago