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faust18 [17]
2 years ago
7

find three consecutive even integers so that the greatest added to three times the least is equal to 84​

Mathematics
1 answer:
Reika [66]2 years ago
3 0

Answer:

26, 28, 30

Step-by-step explanation:

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Match the mathematical expression with its translation
egoroff_w [7]

Answer:

\begin{array}{cc}\text{Mathematical expression}&\text{Translation}\\ \\xy&\text{The product of two numbers}\\ \\\dfrac{x}{y}&x\text{ divided by }y\\ \\x-y&x\text{ minus }y\\ \\x+y&\text{the sum of }x\text{ and }y\\ \\y-x&x\text{ subtracted from }y\\ \\y:x&y\text{ divided by } x\\ \\x+y=6&\text{the sum of two numbers is 6}\\ \\xy=6&\text{the product of two numbers is 6}\\ \\6x=y&\text{6 times a number equals }y\\ \\y=x-6&\text{6 less than a number is }y\end{array}

Step-by-step explanation:

\begin{array}{cc}\text{Mathematical expression}&\text{Translation}\\ \\xy&\text{The product of two numbers}\\ \\\dfrac{x}{y}&x\text{ divided by }y\\ \\x-y&x\text{ minus }y\\ \\x+y&\text{the sum of }x\text{ and }y\\ \\y-x&x\text{ subtracted from }y\\ \\y:x&y\text{ divided by } x\\ \\x+y=6&\text{the sum of two numbers is 6}\\ \\xy=6&\text{the product of two numbers is 6}\\ \\6x=y&\text{6 times a number equals }y\\ \\y=x-6&\text{6 less than a number is }y\end{array}

6 0
3 years ago
conner deposited $84 into his checking account. if his new Balance is $451, what was his balance before the deposit
prisoha [69]
His balance was originally $367 
3 0
3 years ago
Newton's law of cooling is:
Mnenie [13.5K]

Answer:

t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

\frac{du}{dt}= -k (u-T)

We can reorder the expression like this:

\frac{du}{u-T} = -k dt

We can use the substitution w = u-T and dw =du so then we have:

\frac{dw}{w} =-k dt

IF we integrate both sides we got:

ln |w| = -kt +C

If we apply exponential in both sides we got:

w = e^{-kt} *e^c

And if we replace w = u-T we got:

u(t)= T + C_1 e^{-kt}

We can also express the solution in the following terms:

u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}

For this case we know that k =-0.15 hr since w ehave a cooloing, T_{i}= 70 F, T_{amb}=11F, we have this model:

u(t) = (70-11) e^{-0.15t} +11

And if we want that the temperature would be 32F we can solve for t like this:

32 = 59 e^{-0.15 t} +11

21=59 e^{-0.15 t}

\frac{21}{59} = e^{-0.15 t}

If we apply natural logs on both sides we got:

ln (\frac{21}{59}) =-0.15 t

t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr

So it would takes approximately 6.9 hours to reach 32 F.

7 0
3 years ago
Is the student correct?​
Pachacha [2.7K]
Yes the student is correct
6 0
3 years ago
Find the nth degree polynomial function with real coefficients satisfying the given conditions.
RUDIKE [14]
\bf (x+1)(x-3)(x-2-4i)(x-2+4i)
\\\\
\textit{now, let's take a peek at }(x-2-4i)(x-2+4i)\\
\textit{and recall our }\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
(x-2-4i)(x-2+4i)\implies [(x-2)-(4i)][(x-2)+(4i)]
\\\\\
[(x-2)^2-(4i)^2]\implies [(x^2-2x+4)-(4^2\boxed{i^2})]
\\\\\
[(x^2-2x+4)-(16\cdot \boxed{-1})]\implies [(x^2-2x+4)+16]
\\\\
(x^2-2x+20)\\\\
-----------------------------

\bf thus
\\\\

\begin{array}{llll}
(x+1)(x-3)\\(x-2-4i)(x-2+4i)
\end{array}\implies (x+1)(x-3)(x^2-2x+20)
\\\\\\
(x^2-2x-3)(x^2-2x+20)\implies 
\begin{array}{llll}
x^4-2x^3+20x^2-2x^3\\+4x^2-40x+3x^2-6x+60
\end{array}
\\\\\\
x^4-4x^3+27x^2-46x+60
4 0
3 years ago
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