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Arlecino [84]
2 years ago
5

Solve the equation using the Properties of Equality. 12 − c = −10 c =

Mathematics
1 answer:
sergij07 [2.7K]2 years ago
7 0

Answer:

  1. Subtraction Property of Equality
  2. Division Property of Equality
  3. c = 22

Step-by-step explanation:

12 - c = -10

~Subtract 12 to both sides

-c = -22

~Divide -1 to both sides

c = 22

Best of Luck!

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A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side
kari74 [83]

shortest side: 851

middle side:927

longest side : 1306

Explanation

Step 1

Let

x represents the shortest side

y represents the middle side

z represents the longest side

so, set the equations

a) the perimeter of a rectangle is the sum of the sides, so

\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}

b) The shortest side measures 76 mi less than the middle​ side( in other words, you have to subtract 76 from middle side to get the shortest side)

x=y-76\Rightarrow equation(2)

c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)

z=y+379\Rightarrow equation(3)

Step 2

solve the equations

a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\  \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}

now, replace the y value in equatino (2) to find x

b)

\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}

c) finally, prelace x and y value in equation (1) to find z

\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}

so

shortest side: 851

middle side:927

longest side : 1306

I hope this helps you

4 0
11 months ago
What is the following quotient? StartFraction RootIndex 3 StartRoot 60 EndRoot Over RootIndex 3 StartRoot 20 EndRoot EndFraction
FrozenT [24]

Answer:

\sqrt[3]{3}

Step-by-step explanation:

We are required to simplify the quotient: \dfrac{\sqrt[3]{60} }{\sqrt[3]{20}}

Since the <u>numerator and denominator both have the same root index</u>, we can therefore say:

\dfrac{\sqrt[3]{60} }{\sqrt[3]{20}} =\sqrt[3]{\dfrac{60} {20}}

=\sqrt[3]{3}

The simplified form of the given quotient is \sqrt[3]{3}.

6 0
2 years ago
Read 2 more answers
What is the domain of the relation y = arccscx?
Stella [2.4K]

Answer:

y=arc\csc x

Step-by-step explanation:

The given function is y=arc\csc x.

The domain refers to all values of x for which this function is defined.

Recall that: the domain of y=arc \sin (x) is -1\le x\le1

And we know y=arc\csc x is the reciprocal of y=arc \sin (x).

Therefore the complement of the domain of y=arc \sin (x) which is (-\infty,-1]\cup [1,+\infty) is the domain of y=arc\csc x

5 0
2 years ago
The model builder has 4 pieces of balsa wood that are 4 cm, 5 cm, 6 cm, and 7 cm length. How many different combinations of 3 pi
s2008m [1.1K]
About 22 i think hope it helps in any way

7 0
3 years ago
Estimate the quotient: 1628 ÷ 8
Pachacha [2.7K]

Answer:

203.5

Step-by-step explanation:

Please mark brainliest.

4 0
3 years ago
Read 2 more answers
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