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4 years ago

Explain how to solve the equation and then check the solution. 9 = q – 4

Mathematics

2 answers:

ycow [4]4 years ago

7 0

Answer:

Step-by-step explanation:

you take 9 + 4 that gives you 13 witch is q

how you check it is you plug in 13

9 = 13 - 4

Vika [28.1K]4 years ago

5 0

Assignment: $\bold{Solve \ And \ Check \ Equation: \ 9=q-4}$

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Answer: $\boxed{\bold{q=13}}$

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Explanation: $\downarrow\downarrow\downarrow$

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[ Step One ] Switch Sides

$\bold{q-4=9}$

[ Step Two ] Add 4 To Both Sides

$\bold{q-4+4=9+4}$

[ Step Three ] Simplify

$\bold{q=13}$

[ Step Four ] Check Your Work

$\bold{13 \ - \ 4 \ = \ 9}$

[ Step Five ] Question: Is Equation Correct

$\bold{Equation \ Is \ Correct, \ Therefore \ q=13}$

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$\bold{\rightarrow Mordancy \leftarrow}$

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Steven earns extra money babysitting he charges $33 for 4 hours and $57.75 for 7 hours entering an equation to represent the rel

sweet [91]

Answer:

y = 8.25x

Step-by-step explanation:

Linear Modeling

Some events can be modeled as linear functions. If a situation comes where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

$y=mx+b$

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Let's use linear modeling to represent Steven's earnings he makes babysitting. Call y the money he charges by x hours of work.

We know he charges y1=$33 for x1=4 hours, and y2=$57.75 for x2=7 hours. The ordered pairs are (4,33) and ( 7, 57.75)

Computing the equation of the line we have:

$\displaystyle y-33=\frac{57.75-33}{7-4}(x-4)$

Operating:

$\displaystyle y-33=\frac{24.75}{3}(x-4)$

$y - 33 = 8.25( x - 4 )$

$y = 8.25x - 33 + 33$

y = 8.25x

There is a proportional relationship.

6 0

3 years ago

The temperature falls 3 degrees Celsius each hour for 8 hours. What is the total change in temperature over this eight-hour peri

VikaD [51]

Answer:

–24°C

Step-by-step explanation:

(–3°C) × 8 = –24°C

8 0

4 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].

castortr0y [4]

Answer:

The absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0.$

Step-by-step explanation:

Differentiate of $f$ both sides w.r.t. $t$ ,

$f(t)=2 \cos t+\sin 2t$

$\Rightarrow f'(t)=-2\sin t+2\cos 2t$

Now take $f'(t)=0$

$\Rightarrow -2\sin t+2\cos 2t=0$

$\Rightarrow 2\cos 2t=2\sin t$

$\Rightarrow \cos 2t=\sin t$

$\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]$

$\Rightarrow 2\sin ^2t+\sin t-1=0$

$\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0$

$\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0$

$\Rightarrow (\sin t+1)(2\sin t-1)=0$

$\Rightarrow \sin t+1=0 \;\text{and}\; 2\sin t-1=0$

$\Rightarrow \sin t =-1 \;\text{and}\; \sin t =\frac 12$

In the interval $0\leq t\leq \frac {\pi}2$ , the answer to this problem is $\frac {\pi}6$

Now find the second derivative of $f(t)$ w.r.t. $t$ ,

$f''(t)=-2\cos t-4\sin 2t$

$\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3$

Thus, $f(t)$ is maximum at $t=\frac {\pi}6$ and minimum at $t=0$

$\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0$