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3 years ago

Is (4,2) a solution to the system y-x=2 and -3x -2y= -8

1 answer:

3 0

To figure out the answer here, all you have to do is plug the given point into your equations and see if the result is true:

(4, 2) .... aka (x, y)

2 - 4 = 2
-2 = 2 ... this one is FALSE, as -2 doesn't equal 2, so already you can tell that the point won't be a solution, but still, check the second equation.

-3(4) - 2(2) = -8
-12 - 4 = -8
-16 = -8 .... this one is also false. (4, 2) is not a solution for this system of equations.

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Scientists modeled the intensity of the sun, I, as a function of the number of hours since 6:00 a.m., h, using the

MAVERICK [17]

The functions are illustrations of composite functions.

<em>The soil temperature at 2:00pm is 67</em>

The given parameters are:

$\mathbf{I(h) =\frac{12h - h^2}{36}}$ ---- the function for sun intensity

$\mathbf{T(I) =\sqrt{5000I}}$ -- the function for temperature

At 2:00pm, the value of h (number of hours) is:

$\mathbf{h = 2:00pm - 6:00am}$

$\mathbf{h = 8}$

Substitute 8 for h in $\mathbf{I(h) =\frac{12h - h^2}{36}}$ , to calculate the sun intensity

$\mathbf{I(8) =\frac{12 \times 8 - 8^2}{36}}$

$\mathbf{I(8) =\frac{32}{36}}$

$\mathbf{I(8) =\frac{8}{9}}$

Substitute 8/9 for I in $\mathbf{T(I) =\sqrt{5000I}}$ , to calculate the temperature of the soil

$\mathbf{T(8/9) =\sqrt{5000 \times 8/9}}$

$\mathbf{T(8/9) =\sqrt{4444.44}}$

$\mathbf{T(8/9) =66.67}$

Approximate

$\mathbf{T(8/9) =67}$

Hence, the soil temperature at 2:00pm is 67

Read more about composite functions at:

brainly.com/question/20379727

5 0

2 years ago

Find x so that (x,-14) is a solution to 2x+3y=12

Monica [59]

Answer:

Question:

Find $x$ so that $(x,-14)$ is a solution to $2x+3y=12$ .

Step-by-step explanation:

So we are asked to replace $y$ with -14 and solve for $x$ in the equation:

$2x+3y=12$ .

$2x+3y=12$ with $y=-14$ :

$2x+3(-14)=12$

$2x-42=12$

Add 42 on both sides:

$2x=54$

Divide both sides by 2:

$x=27$ .

So the $x$ -coordinate that corresponding to $y=-14$ is $27$ .

Verify that:

$(27,-14)$ is a point satisfying $2x+3y=12$ .

Replace $x$ with 27 and $y$ with -14:

$2(27)+3(-14)=12$

$54+-42=12$

$12=12$ is true so our work must be right.

3 0

3 years ago

Bella bought packs of stickers to give to her friends. Each pack cost $4. She spent a total of

Shalnov [3]

Answer:

8 packs

Step-by-step explanation:

$4 = 1 pack

$32 = ?

$32 = $32/$4

$32 = 8 packs

4 0

3 years ago

Four adults and 5 children go to see a movie and buy $15 worth of concessions. The total cost of their trip is $71. If each chil

NNADVOKAT [17]

Answer:$7.75 Take the 5 tickets at $5 to get $25. Add the $15 for concessions to reach $40. Subtract $40 from the 71 spent to get $31. Now divide the 31 by 4 for the amount of adults which equals $7.75

Step-by-step explanation:

4 0

3 years ago

Find log_{3} [27*\sqrt[4]{3} ] wihout using a calculator. Please show all work!

Zigmanuir [339]

$\bf \textit{logarithm of factors}
\\\\
log_a(xy)\implies log_a(x)+log_a(y)\\\\
-------------------------------\\\\
log_3(27\sqrt[3]{3})\qquad 
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
\sqrt[3]{3}=\sqrt[3]{3^1}\\
\qquad 3^{\frac{1}{3}}
\end{cases}\implies log_3\left( 3^3\cdot 3^{\frac{1}{3}} \right)
\\\\\\
log_3\left( 3^{3+\frac{1}{3}} \right)\implies log_3\left( 3^{\frac{4}{3}} \right)\implies \cfrac{4}{3}\cdot log_3(3)\implies \cfrac{4}{3}\cdot 1\implies \cfrac{4}{3}$

4 0

3 years ago